367302
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?
Now by principle of homogeneity of dimensions L.H.S and R.H.S of (1), (2) and (4) will be same and is \(L\). For (3) \([L . H . S]=L \quad[\) R.H.S \(]=\dfrac{L}{T}=L T^{-1}\) \([\) L.H.S \(] \neq[\) R.H.S \(]\) Hence, (3) is not correct answer.
PHXI02:UNITS AND MEASUREMENTS
367303
The dimensional formula of product and quotient of two physical quantities \(A\) and \(B\) are given by \([AB] = [M{L^2}{T^{ - 2}}]\) and \(\left[ {\frac{A}{B}} \right] = M{T^{ - 2}}\). Find the quantities \(A\) and \(B\)
367304
A force defined by \({F=\alpha t^{2}+\beta t}\) acts on a particle at a given time \({t}\). The factor which is dimensionless, if \({\alpha}\) and \({\beta}\) are constants, is:
1 \({\beta t / \alpha}\)
2 \({\alpha t / \beta}\)
3 \({\alpha \beta t}\)
4 \({\alpha \beta / t}\)
Explanation:
From principle of homogeneity The dimensions of the following quantities must be same. \({[F]=\left[\alpha t^{2}\right]=[\beta t]}\) \({[\alpha]=\dfrac{[F]}{\left[t^{2}\right]}}\) and \({[\beta]=\dfrac{[F]}{[t]}}\) \({\therefore[\alpha][t]=[\beta]}\) \({\therefore \dfrac{\alpha t}{\beta}=}\) dimensionless
NEET - 2024
PHXI02:UNITS AND MEASUREMENTS
367305
The equation \({\left(P+\dfrac{a}{V^{2}}\right)(V-b)=}\) constant. The units of \({a}\) are
1 \({d y n \times {cm}^{5}}\)
2 \({d y n \times {cm}^{4}}\)
3 \({{dyn} / {cm}^{3}}\)
4 \({{dyn} / {cm}^{2}}\)
Explanation:
Unit of \({a=}\) unit of \({P \times}\) unit of \({V^{2}}\) \({=\dfrac{d y n e}{{~cm}^{2}} \times\left({cm}^{3}\right)^{2}}\) \( = dyne \times c{m^4}\)
367302
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?
Now by principle of homogeneity of dimensions L.H.S and R.H.S of (1), (2) and (4) will be same and is \(L\). For (3) \([L . H . S]=L \quad[\) R.H.S \(]=\dfrac{L}{T}=L T^{-1}\) \([\) L.H.S \(] \neq[\) R.H.S \(]\) Hence, (3) is not correct answer.
PHXI02:UNITS AND MEASUREMENTS
367303
The dimensional formula of product and quotient of two physical quantities \(A\) and \(B\) are given by \([AB] = [M{L^2}{T^{ - 2}}]\) and \(\left[ {\frac{A}{B}} \right] = M{T^{ - 2}}\). Find the quantities \(A\) and \(B\)
367304
A force defined by \({F=\alpha t^{2}+\beta t}\) acts on a particle at a given time \({t}\). The factor which is dimensionless, if \({\alpha}\) and \({\beta}\) are constants, is:
1 \({\beta t / \alpha}\)
2 \({\alpha t / \beta}\)
3 \({\alpha \beta t}\)
4 \({\alpha \beta / t}\)
Explanation:
From principle of homogeneity The dimensions of the following quantities must be same. \({[F]=\left[\alpha t^{2}\right]=[\beta t]}\) \({[\alpha]=\dfrac{[F]}{\left[t^{2}\right]}}\) and \({[\beta]=\dfrac{[F]}{[t]}}\) \({\therefore[\alpha][t]=[\beta]}\) \({\therefore \dfrac{\alpha t}{\beta}=}\) dimensionless
NEET - 2024
PHXI02:UNITS AND MEASUREMENTS
367305
The equation \({\left(P+\dfrac{a}{V^{2}}\right)(V-b)=}\) constant. The units of \({a}\) are
1 \({d y n \times {cm}^{5}}\)
2 \({d y n \times {cm}^{4}}\)
3 \({{dyn} / {cm}^{3}}\)
4 \({{dyn} / {cm}^{2}}\)
Explanation:
Unit of \({a=}\) unit of \({P \times}\) unit of \({V^{2}}\) \({=\dfrac{d y n e}{{~cm}^{2}} \times\left({cm}^{3}\right)^{2}}\) \( = dyne \times c{m^4}\)
367302
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?
Now by principle of homogeneity of dimensions L.H.S and R.H.S of (1), (2) and (4) will be same and is \(L\). For (3) \([L . H . S]=L \quad[\) R.H.S \(]=\dfrac{L}{T}=L T^{-1}\) \([\) L.H.S \(] \neq[\) R.H.S \(]\) Hence, (3) is not correct answer.
PHXI02:UNITS AND MEASUREMENTS
367303
The dimensional formula of product and quotient of two physical quantities \(A\) and \(B\) are given by \([AB] = [M{L^2}{T^{ - 2}}]\) and \(\left[ {\frac{A}{B}} \right] = M{T^{ - 2}}\). Find the quantities \(A\) and \(B\)
367304
A force defined by \({F=\alpha t^{2}+\beta t}\) acts on a particle at a given time \({t}\). The factor which is dimensionless, if \({\alpha}\) and \({\beta}\) are constants, is:
1 \({\beta t / \alpha}\)
2 \({\alpha t / \beta}\)
3 \({\alpha \beta t}\)
4 \({\alpha \beta / t}\)
Explanation:
From principle of homogeneity The dimensions of the following quantities must be same. \({[F]=\left[\alpha t^{2}\right]=[\beta t]}\) \({[\alpha]=\dfrac{[F]}{\left[t^{2}\right]}}\) and \({[\beta]=\dfrac{[F]}{[t]}}\) \({\therefore[\alpha][t]=[\beta]}\) \({\therefore \dfrac{\alpha t}{\beta}=}\) dimensionless
NEET - 2024
PHXI02:UNITS AND MEASUREMENTS
367305
The equation \({\left(P+\dfrac{a}{V^{2}}\right)(V-b)=}\) constant. The units of \({a}\) are
1 \({d y n \times {cm}^{5}}\)
2 \({d y n \times {cm}^{4}}\)
3 \({{dyn} / {cm}^{3}}\)
4 \({{dyn} / {cm}^{2}}\)
Explanation:
Unit of \({a=}\) unit of \({P \times}\) unit of \({V^{2}}\) \({=\dfrac{d y n e}{{~cm}^{2}} \times\left({cm}^{3}\right)^{2}}\) \( = dyne \times c{m^4}\)
367302
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?
Now by principle of homogeneity of dimensions L.H.S and R.H.S of (1), (2) and (4) will be same and is \(L\). For (3) \([L . H . S]=L \quad[\) R.H.S \(]=\dfrac{L}{T}=L T^{-1}\) \([\) L.H.S \(] \neq[\) R.H.S \(]\) Hence, (3) is not correct answer.
PHXI02:UNITS AND MEASUREMENTS
367303
The dimensional formula of product and quotient of two physical quantities \(A\) and \(B\) are given by \([AB] = [M{L^2}{T^{ - 2}}]\) and \(\left[ {\frac{A}{B}} \right] = M{T^{ - 2}}\). Find the quantities \(A\) and \(B\)
367304
A force defined by \({F=\alpha t^{2}+\beta t}\) acts on a particle at a given time \({t}\). The factor which is dimensionless, if \({\alpha}\) and \({\beta}\) are constants, is:
1 \({\beta t / \alpha}\)
2 \({\alpha t / \beta}\)
3 \({\alpha \beta t}\)
4 \({\alpha \beta / t}\)
Explanation:
From principle of homogeneity The dimensions of the following quantities must be same. \({[F]=\left[\alpha t^{2}\right]=[\beta t]}\) \({[\alpha]=\dfrac{[F]}{\left[t^{2}\right]}}\) and \({[\beta]=\dfrac{[F]}{[t]}}\) \({\therefore[\alpha][t]=[\beta]}\) \({\therefore \dfrac{\alpha t}{\beta}=}\) dimensionless
NEET - 2024
PHXI02:UNITS AND MEASUREMENTS
367305
The equation \({\left(P+\dfrac{a}{V^{2}}\right)(V-b)=}\) constant. The units of \({a}\) are
1 \({d y n \times {cm}^{5}}\)
2 \({d y n \times {cm}^{4}}\)
3 \({{dyn} / {cm}^{3}}\)
4 \({{dyn} / {cm}^{2}}\)
Explanation:
Unit of \({a=}\) unit of \({P \times}\) unit of \({V^{2}}\) \({=\dfrac{d y n e}{{~cm}^{2}} \times\left({cm}^{3}\right)^{2}}\) \( = dyne \times c{m^4}\)
