139495
The frequency of vibration \(f\) of a mass \(m\) suspended from a spring of spring constant \(k\) is given by a relation of the type \(f=\mathbf{C m}^{x} k^{y}\), where \(C\) is a dimensionless constant. The values of \(x\) and \(y\) are
D Given, \(\mathrm{f}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) where, \(\mathrm{C}=\) dimensionless constant \(\mathrm{m}=\text { mass }\) \(\mathrm{K}=\text { spring constant }\) The dimension of frequency, \(\mathrm{f}=\left[\mathrm{T}^{-1}\right]\) The dimension of mass, \(m=[\mathrm{M}]\) The dimension of spring constant, \(\mathrm{k}=\left[\mathrm{MT}^{-2}\right]\) \(\mathrm{F}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=[\mathrm{M}]^{\mathrm{x}}\left[\mathrm{MT}^{-2}\right]^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=\left[\mathrm{M}^{\mathrm{x}+\mathrm{y}} \cdot \mathrm{T}^{-2 \mathrm{y}}\right]\) \(\mathrm{x}+\mathrm{y}=0\) and \(-2 \mathrm{y}=-1\) \(\mathrm{x}=-\mathrm{y}\) and \(\mathrm{y}=\frac{1}{2}\) \(\Rightarrow \mathrm{x}=-\frac{1}{2}, \mathrm{y}=\frac{1}{2}\)
AIPMT 1990
Units and Measurements
139496
If \(C\) and \(R\) denote capacitance and resistance respectively, then the dimensional formula of CR is
A Capacitance \((\mathrm{C})=\frac{\mathrm{q}}{\mathrm{v}}=\frac{\mathrm{q}}{\frac{\mathrm{w}}{\mathrm{q}}}=\frac{\mathrm{q}^{2}}{\mathrm{w}}=\frac{(\text { it })^{2}}{\text { F.d }}\) Where \(\mathrm{q}=\) charge \(\mathrm{C}=\text { Capacitance }\) \(\mathrm{v}=\text { voltage }\) \(=\frac{(\text { it })^{2}}{\mathrm{Fx}}=\frac{[\mathrm{AT}]^{2}}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) and \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}=\frac{\mathrm{W}}{\mathrm{qi} \mathrm{i}}=\frac{\mathrm{F} \cdot \mathrm{d}}{\mathrm{i}^{2} \cdot \mathrm{t}}=\frac{\left[\mathrm{MLT}^{-2}\right][\mathrm{L}]}{[\mathrm{A}]^{2}[\mathrm{~T}]}\) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) Dimensional formula of \(\mathrm{CR}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1}\right]\)
AIPMT-1995
Units and Measurements
139498
If power (P), surface, tension (T) and Planck's constant (h) are arranged, so that the dimensions of time in their dimensional formulae are in ascending order, then which of the following is correct?
1 \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
2 \(\mathrm{P}, \mathrm{h}, \mathrm{T}\)
3 \(\mathrm{T}, \mathrm{P}, \mathrm{h}\)
4 \(\mathrm{T}, \mathrm{h}, \mathrm{p}\)
Explanation:
A Power \(\mathrm{P}=\frac{\mathrm{W}}{\mathrm{T}}\) \([\mathrm{P}]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{T}]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]\) Surface Tension, \(T=\frac{F}{L}\) \([\mathrm{T}]=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{L}]}=\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right]\) Photon energy, \(\mathrm{E}=\mathrm{h} \nu\) Planck's constant \(=\mathrm{h}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{\left[\mathrm{T}^{-1}\right]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]\) \(\therefore\) The ascending order of dimensions of time in the dimensional formula \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
C Formula of latent heat given by \(L=\frac{Q}{m}\) Where, \(\mathrm{L}=\) latent heat \(\mathrm{Q}=\) amount of heat \(\mathrm{M}=\) mass of substance Dimension of heat or work \(=\) force \(\times\) displacement \(=\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}\right][\mathrm{L}]\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]\) Dimension of mass \(=[\mathrm{M}]\) Dimension of Latent heat \(L=\frac{\operatorname{dim} . \text { of } Q}{\operatorname{dim} . \text { of } m}\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right] \cdot[\mathrm{M}]^{-1}\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]\)
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Units and Measurements
139495
The frequency of vibration \(f\) of a mass \(m\) suspended from a spring of spring constant \(k\) is given by a relation of the type \(f=\mathbf{C m}^{x} k^{y}\), where \(C\) is a dimensionless constant. The values of \(x\) and \(y\) are
D Given, \(\mathrm{f}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) where, \(\mathrm{C}=\) dimensionless constant \(\mathrm{m}=\text { mass }\) \(\mathrm{K}=\text { spring constant }\) The dimension of frequency, \(\mathrm{f}=\left[\mathrm{T}^{-1}\right]\) The dimension of mass, \(m=[\mathrm{M}]\) The dimension of spring constant, \(\mathrm{k}=\left[\mathrm{MT}^{-2}\right]\) \(\mathrm{F}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=[\mathrm{M}]^{\mathrm{x}}\left[\mathrm{MT}^{-2}\right]^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=\left[\mathrm{M}^{\mathrm{x}+\mathrm{y}} \cdot \mathrm{T}^{-2 \mathrm{y}}\right]\) \(\mathrm{x}+\mathrm{y}=0\) and \(-2 \mathrm{y}=-1\) \(\mathrm{x}=-\mathrm{y}\) and \(\mathrm{y}=\frac{1}{2}\) \(\Rightarrow \mathrm{x}=-\frac{1}{2}, \mathrm{y}=\frac{1}{2}\)
AIPMT 1990
Units and Measurements
139496
If \(C\) and \(R\) denote capacitance and resistance respectively, then the dimensional formula of CR is
A Capacitance \((\mathrm{C})=\frac{\mathrm{q}}{\mathrm{v}}=\frac{\mathrm{q}}{\frac{\mathrm{w}}{\mathrm{q}}}=\frac{\mathrm{q}^{2}}{\mathrm{w}}=\frac{(\text { it })^{2}}{\text { F.d }}\) Where \(\mathrm{q}=\) charge \(\mathrm{C}=\text { Capacitance }\) \(\mathrm{v}=\text { voltage }\) \(=\frac{(\text { it })^{2}}{\mathrm{Fx}}=\frac{[\mathrm{AT}]^{2}}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) and \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}=\frac{\mathrm{W}}{\mathrm{qi} \mathrm{i}}=\frac{\mathrm{F} \cdot \mathrm{d}}{\mathrm{i}^{2} \cdot \mathrm{t}}=\frac{\left[\mathrm{MLT}^{-2}\right][\mathrm{L}]}{[\mathrm{A}]^{2}[\mathrm{~T}]}\) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) Dimensional formula of \(\mathrm{CR}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1}\right]\)
AIPMT-1995
Units and Measurements
139498
If power (P), surface, tension (T) and Planck's constant (h) are arranged, so that the dimensions of time in their dimensional formulae are in ascending order, then which of the following is correct?
1 \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
2 \(\mathrm{P}, \mathrm{h}, \mathrm{T}\)
3 \(\mathrm{T}, \mathrm{P}, \mathrm{h}\)
4 \(\mathrm{T}, \mathrm{h}, \mathrm{p}\)
Explanation:
A Power \(\mathrm{P}=\frac{\mathrm{W}}{\mathrm{T}}\) \([\mathrm{P}]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{T}]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]\) Surface Tension, \(T=\frac{F}{L}\) \([\mathrm{T}]=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{L}]}=\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right]\) Photon energy, \(\mathrm{E}=\mathrm{h} \nu\) Planck's constant \(=\mathrm{h}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{\left[\mathrm{T}^{-1}\right]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]\) \(\therefore\) The ascending order of dimensions of time in the dimensional formula \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
C Formula of latent heat given by \(L=\frac{Q}{m}\) Where, \(\mathrm{L}=\) latent heat \(\mathrm{Q}=\) amount of heat \(\mathrm{M}=\) mass of substance Dimension of heat or work \(=\) force \(\times\) displacement \(=\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}\right][\mathrm{L}]\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]\) Dimension of mass \(=[\mathrm{M}]\) Dimension of Latent heat \(L=\frac{\operatorname{dim} . \text { of } Q}{\operatorname{dim} . \text { of } m}\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right] \cdot[\mathrm{M}]^{-1}\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]\)
139495
The frequency of vibration \(f\) of a mass \(m\) suspended from a spring of spring constant \(k\) is given by a relation of the type \(f=\mathbf{C m}^{x} k^{y}\), where \(C\) is a dimensionless constant. The values of \(x\) and \(y\) are
D Given, \(\mathrm{f}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) where, \(\mathrm{C}=\) dimensionless constant \(\mathrm{m}=\text { mass }\) \(\mathrm{K}=\text { spring constant }\) The dimension of frequency, \(\mathrm{f}=\left[\mathrm{T}^{-1}\right]\) The dimension of mass, \(m=[\mathrm{M}]\) The dimension of spring constant, \(\mathrm{k}=\left[\mathrm{MT}^{-2}\right]\) \(\mathrm{F}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=[\mathrm{M}]^{\mathrm{x}}\left[\mathrm{MT}^{-2}\right]^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=\left[\mathrm{M}^{\mathrm{x}+\mathrm{y}} \cdot \mathrm{T}^{-2 \mathrm{y}}\right]\) \(\mathrm{x}+\mathrm{y}=0\) and \(-2 \mathrm{y}=-1\) \(\mathrm{x}=-\mathrm{y}\) and \(\mathrm{y}=\frac{1}{2}\) \(\Rightarrow \mathrm{x}=-\frac{1}{2}, \mathrm{y}=\frac{1}{2}\)
AIPMT 1990
Units and Measurements
139496
If \(C\) and \(R\) denote capacitance and resistance respectively, then the dimensional formula of CR is
A Capacitance \((\mathrm{C})=\frac{\mathrm{q}}{\mathrm{v}}=\frac{\mathrm{q}}{\frac{\mathrm{w}}{\mathrm{q}}}=\frac{\mathrm{q}^{2}}{\mathrm{w}}=\frac{(\text { it })^{2}}{\text { F.d }}\) Where \(\mathrm{q}=\) charge \(\mathrm{C}=\text { Capacitance }\) \(\mathrm{v}=\text { voltage }\) \(=\frac{(\text { it })^{2}}{\mathrm{Fx}}=\frac{[\mathrm{AT}]^{2}}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) and \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}=\frac{\mathrm{W}}{\mathrm{qi} \mathrm{i}}=\frac{\mathrm{F} \cdot \mathrm{d}}{\mathrm{i}^{2} \cdot \mathrm{t}}=\frac{\left[\mathrm{MLT}^{-2}\right][\mathrm{L}]}{[\mathrm{A}]^{2}[\mathrm{~T}]}\) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) Dimensional formula of \(\mathrm{CR}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1}\right]\)
AIPMT-1995
Units and Measurements
139498
If power (P), surface, tension (T) and Planck's constant (h) are arranged, so that the dimensions of time in their dimensional formulae are in ascending order, then which of the following is correct?
1 \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
2 \(\mathrm{P}, \mathrm{h}, \mathrm{T}\)
3 \(\mathrm{T}, \mathrm{P}, \mathrm{h}\)
4 \(\mathrm{T}, \mathrm{h}, \mathrm{p}\)
Explanation:
A Power \(\mathrm{P}=\frac{\mathrm{W}}{\mathrm{T}}\) \([\mathrm{P}]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{T}]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]\) Surface Tension, \(T=\frac{F}{L}\) \([\mathrm{T}]=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{L}]}=\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right]\) Photon energy, \(\mathrm{E}=\mathrm{h} \nu\) Planck's constant \(=\mathrm{h}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{\left[\mathrm{T}^{-1}\right]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]\) \(\therefore\) The ascending order of dimensions of time in the dimensional formula \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
C Formula of latent heat given by \(L=\frac{Q}{m}\) Where, \(\mathrm{L}=\) latent heat \(\mathrm{Q}=\) amount of heat \(\mathrm{M}=\) mass of substance Dimension of heat or work \(=\) force \(\times\) displacement \(=\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}\right][\mathrm{L}]\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]\) Dimension of mass \(=[\mathrm{M}]\) Dimension of Latent heat \(L=\frac{\operatorname{dim} . \text { of } Q}{\operatorname{dim} . \text { of } m}\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right] \cdot[\mathrm{M}]^{-1}\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]\)
139495
The frequency of vibration \(f\) of a mass \(m\) suspended from a spring of spring constant \(k\) is given by a relation of the type \(f=\mathbf{C m}^{x} k^{y}\), where \(C\) is a dimensionless constant. The values of \(x\) and \(y\) are
D Given, \(\mathrm{f}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) where, \(\mathrm{C}=\) dimensionless constant \(\mathrm{m}=\text { mass }\) \(\mathrm{K}=\text { spring constant }\) The dimension of frequency, \(\mathrm{f}=\left[\mathrm{T}^{-1}\right]\) The dimension of mass, \(m=[\mathrm{M}]\) The dimension of spring constant, \(\mathrm{k}=\left[\mathrm{MT}^{-2}\right]\) \(\mathrm{F}=\mathrm{Cm}^{\mathrm{x}} \cdot \mathrm{K}^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=[\mathrm{M}]^{\mathrm{x}}\left[\mathrm{MT}^{-2}\right]^{\mathrm{y}}\) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]=\left[\mathrm{M}^{\mathrm{x}+\mathrm{y}} \cdot \mathrm{T}^{-2 \mathrm{y}}\right]\) \(\mathrm{x}+\mathrm{y}=0\) and \(-2 \mathrm{y}=-1\) \(\mathrm{x}=-\mathrm{y}\) and \(\mathrm{y}=\frac{1}{2}\) \(\Rightarrow \mathrm{x}=-\frac{1}{2}, \mathrm{y}=\frac{1}{2}\)
AIPMT 1990
Units and Measurements
139496
If \(C\) and \(R\) denote capacitance and resistance respectively, then the dimensional formula of CR is
A Capacitance \((\mathrm{C})=\frac{\mathrm{q}}{\mathrm{v}}=\frac{\mathrm{q}}{\frac{\mathrm{w}}{\mathrm{q}}}=\frac{\mathrm{q}^{2}}{\mathrm{w}}=\frac{(\text { it })^{2}}{\text { F.d }}\) Where \(\mathrm{q}=\) charge \(\mathrm{C}=\text { Capacitance }\) \(\mathrm{v}=\text { voltage }\) \(=\frac{(\text { it })^{2}}{\mathrm{Fx}}=\frac{[\mathrm{AT}]^{2}}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) and \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}=\frac{\mathrm{W}}{\mathrm{qi} \mathrm{i}}=\frac{\mathrm{F} \cdot \mathrm{d}}{\mathrm{i}^{2} \cdot \mathrm{t}}=\frac{\left[\mathrm{MLT}^{-2}\right][\mathrm{L}]}{[\mathrm{A}]^{2}[\mathrm{~T}]}\) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) Dimensional formula of \(\mathrm{CR}\) \(=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1}\right]\)
AIPMT-1995
Units and Measurements
139498
If power (P), surface, tension (T) and Planck's constant (h) are arranged, so that the dimensions of time in their dimensional formulae are in ascending order, then which of the following is correct?
1 \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
2 \(\mathrm{P}, \mathrm{h}, \mathrm{T}\)
3 \(\mathrm{T}, \mathrm{P}, \mathrm{h}\)
4 \(\mathrm{T}, \mathrm{h}, \mathrm{p}\)
Explanation:
A Power \(\mathrm{P}=\frac{\mathrm{W}}{\mathrm{T}}\) \([\mathrm{P}]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{T}]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]\) Surface Tension, \(T=\frac{F}{L}\) \([\mathrm{T}]=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{L}]}=\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right]\) Photon energy, \(\mathrm{E}=\mathrm{h} \nu\) Planck's constant \(=\mathrm{h}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{\left[\mathrm{T}^{-1}\right]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]\) \(\therefore\) The ascending order of dimensions of time in the dimensional formula \(\mathrm{P}, \mathrm{T}, \mathrm{h}\)
C Formula of latent heat given by \(L=\frac{Q}{m}\) Where, \(\mathrm{L}=\) latent heat \(\mathrm{Q}=\) amount of heat \(\mathrm{M}=\) mass of substance Dimension of heat or work \(=\) force \(\times\) displacement \(=\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}\right][\mathrm{L}]\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]\) Dimension of mass \(=[\mathrm{M}]\) Dimension of Latent heat \(L=\frac{\operatorname{dim} . \text { of } Q}{\operatorname{dim} . \text { of } m}\) \(=\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right] \cdot[\mathrm{M}]^{-1}\) \(=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]\)