Dimensions
PHXI02:UNITS AND MEASUREMENTS

367310 The equation of state of a real gas is given by \(\left(P+\dfrac{a}{V^{2}}\right)(V-b)=R T\), where \(P, V\) and \(T\) are pressure, volume and temperature respectively and \(R\) is the universal gas constant. The dimension of \(\dfrac{a}{b^{2}}\) is similar to that of:

1 \(R T\)
2 \(P V\)
3 \(R\)
4 \(P\)
PHXI02:UNITS AND MEASUREMENTS

367311 The force ‘\(F\)’ acting on a body of density ‘\(d\)’ are related by the relation \(F = \frac{y}{{\sqrt d }}\) . The dimensions of ‘ \(y\)’ are

1 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
2 \(\left[ {{L^{ - 1}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
3 \(\left[ {{L^{ - 1}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
4 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
PHXI02:UNITS AND MEASUREMENTS

367312 The velocity " \(V\) " of a particle is given in terms of time \(t\) as \(V=a t+\dfrac{b}{t+C}\).The dimensions of \(a, b, c\) are:

1 \(L^2 ; M L ; T^{-2}\)
2 \(L T^2 ; L T ; L\)
3 \(L T^{-2} ; L ; T\)
4 \(L ; L T ; T^2\)
PHXI02:UNITS AND MEASUREMENTS

367313 The potential energy of a particle varies with distance \(x\) as \(U=\dfrac{A x^{1 / 2}}{x^{2}+B}\), where \(A\) and \(B\) are constants. The dimensional formula for \(A \times B\) is

1 \(\left[M^{1} L^{7 / 2} T^{-2}\right]\)
2 \(\left[M^{1} L^{1 / 2} T^{-2}\right]\)
3 \(\left[M^{1} L^{5 / 2} T^{-2}\right]\)
4 \(\left[M^{1} L^{9 / 2} T^{-2}\right]\)
PHXI02:UNITS AND MEASUREMENTS

367314 Suppose \(A = {B^n}{C^m}\) , where \(A\) has dimensions \(LT\), \(B\) has dimensions \({L^2}{T^{ - 1}}\), and \(C\) has dimensions \(L{T^2}\). Then find the values of exponents \(n\) and \(m\) :

1 \(\frac{2}{5},\frac{4}{5}\)
2 \(\frac{2}{5},\frac{3}{5}\)
3 \(\frac{3}{5},\frac{1}{5}\)
4 \(\frac{1}{5},\frac{3}{5}\)
PHXI02:UNITS AND MEASUREMENTS

367310 The equation of state of a real gas is given by \(\left(P+\dfrac{a}{V^{2}}\right)(V-b)=R T\), where \(P, V\) and \(T\) are pressure, volume and temperature respectively and \(R\) is the universal gas constant. The dimension of \(\dfrac{a}{b^{2}}\) is similar to that of:

1 \(R T\)
2 \(P V\)
3 \(R\)
4 \(P\)
PHXI02:UNITS AND MEASUREMENTS

367311 The force ‘\(F\)’ acting on a body of density ‘\(d\)’ are related by the relation \(F = \frac{y}{{\sqrt d }}\) . The dimensions of ‘ \(y\)’ are

1 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
2 \(\left[ {{L^{ - 1}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
3 \(\left[ {{L^{ - 1}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
4 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
PHXI02:UNITS AND MEASUREMENTS

367312 The velocity " \(V\) " of a particle is given in terms of time \(t\) as \(V=a t+\dfrac{b}{t+C}\).The dimensions of \(a, b, c\) are:

1 \(L^2 ; M L ; T^{-2}\)
2 \(L T^2 ; L T ; L\)
3 \(L T^{-2} ; L ; T\)
4 \(L ; L T ; T^2\)
PHXI02:UNITS AND MEASUREMENTS

367313 The potential energy of a particle varies with distance \(x\) as \(U=\dfrac{A x^{1 / 2}}{x^{2}+B}\), where \(A\) and \(B\) are constants. The dimensional formula for \(A \times B\) is

1 \(\left[M^{1} L^{7 / 2} T^{-2}\right]\)
2 \(\left[M^{1} L^{1 / 2} T^{-2}\right]\)
3 \(\left[M^{1} L^{5 / 2} T^{-2}\right]\)
4 \(\left[M^{1} L^{9 / 2} T^{-2}\right]\)
PHXI02:UNITS AND MEASUREMENTS

367314 Suppose \(A = {B^n}{C^m}\) , where \(A\) has dimensions \(LT\), \(B\) has dimensions \({L^2}{T^{ - 1}}\), and \(C\) has dimensions \(L{T^2}\). Then find the values of exponents \(n\) and \(m\) :

1 \(\frac{2}{5},\frac{4}{5}\)
2 \(\frac{2}{5},\frac{3}{5}\)
3 \(\frac{3}{5},\frac{1}{5}\)
4 \(\frac{1}{5},\frac{3}{5}\)
PHXI02:UNITS AND MEASUREMENTS

367310 The equation of state of a real gas is given by \(\left(P+\dfrac{a}{V^{2}}\right)(V-b)=R T\), where \(P, V\) and \(T\) are pressure, volume and temperature respectively and \(R\) is the universal gas constant. The dimension of \(\dfrac{a}{b^{2}}\) is similar to that of:

1 \(R T\)
2 \(P V\)
3 \(R\)
4 \(P\)
PHXI02:UNITS AND MEASUREMENTS

367311 The force ‘\(F\)’ acting on a body of density ‘\(d\)’ are related by the relation \(F = \frac{y}{{\sqrt d }}\) . The dimensions of ‘ \(y\)’ are

1 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
2 \(\left[ {{L^{ - 1}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
3 \(\left[ {{L^{ - 1}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
4 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
PHXI02:UNITS AND MEASUREMENTS

367312 The velocity " \(V\) " of a particle is given in terms of time \(t\) as \(V=a t+\dfrac{b}{t+C}\).The dimensions of \(a, b, c\) are:

1 \(L^2 ; M L ; T^{-2}\)
2 \(L T^2 ; L T ; L\)
3 \(L T^{-2} ; L ; T\)
4 \(L ; L T ; T^2\)
PHXI02:UNITS AND MEASUREMENTS

367313 The potential energy of a particle varies with distance \(x\) as \(U=\dfrac{A x^{1 / 2}}{x^{2}+B}\), where \(A\) and \(B\) are constants. The dimensional formula for \(A \times B\) is

1 \(\left[M^{1} L^{7 / 2} T^{-2}\right]\)
2 \(\left[M^{1} L^{1 / 2} T^{-2}\right]\)
3 \(\left[M^{1} L^{5 / 2} T^{-2}\right]\)
4 \(\left[M^{1} L^{9 / 2} T^{-2}\right]\)
PHXI02:UNITS AND MEASUREMENTS

367314 Suppose \(A = {B^n}{C^m}\) , where \(A\) has dimensions \(LT\), \(B\) has dimensions \({L^2}{T^{ - 1}}\), and \(C\) has dimensions \(L{T^2}\). Then find the values of exponents \(n\) and \(m\) :

1 \(\frac{2}{5},\frac{4}{5}\)
2 \(\frac{2}{5},\frac{3}{5}\)
3 \(\frac{3}{5},\frac{1}{5}\)
4 \(\frac{1}{5},\frac{3}{5}\)
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PHXI02:UNITS AND MEASUREMENTS

367310 The equation of state of a real gas is given by \(\left(P+\dfrac{a}{V^{2}}\right)(V-b)=R T\), where \(P, V\) and \(T\) are pressure, volume and temperature respectively and \(R\) is the universal gas constant. The dimension of \(\dfrac{a}{b^{2}}\) is similar to that of:

1 \(R T\)
2 \(P V\)
3 \(R\)
4 \(P\)
PHXI02:UNITS AND MEASUREMENTS

367311 The force ‘\(F\)’ acting on a body of density ‘\(d\)’ are related by the relation \(F = \frac{y}{{\sqrt d }}\) . The dimensions of ‘ \(y\)’ are

1 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
2 \(\left[ {{L^{ - 1}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
3 \(\left[ {{L^{ - 1}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
4 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
PHXI02:UNITS AND MEASUREMENTS

367312 The velocity " \(V\) " of a particle is given in terms of time \(t\) as \(V=a t+\dfrac{b}{t+C}\).The dimensions of \(a, b, c\) are:

1 \(L^2 ; M L ; T^{-2}\)
2 \(L T^2 ; L T ; L\)
3 \(L T^{-2} ; L ; T\)
4 \(L ; L T ; T^2\)
PHXI02:UNITS AND MEASUREMENTS

367313 The potential energy of a particle varies with distance \(x\) as \(U=\dfrac{A x^{1 / 2}}{x^{2}+B}\), where \(A\) and \(B\) are constants. The dimensional formula for \(A \times B\) is

1 \(\left[M^{1} L^{7 / 2} T^{-2}\right]\)
2 \(\left[M^{1} L^{1 / 2} T^{-2}\right]\)
3 \(\left[M^{1} L^{5 / 2} T^{-2}\right]\)
4 \(\left[M^{1} L^{9 / 2} T^{-2}\right]\)
PHXI02:UNITS AND MEASUREMENTS

367314 Suppose \(A = {B^n}{C^m}\) , where \(A\) has dimensions \(LT\), \(B\) has dimensions \({L^2}{T^{ - 1}}\), and \(C\) has dimensions \(L{T^2}\). Then find the values of exponents \(n\) and \(m\) :

1 \(\frac{2}{5},\frac{4}{5}\)
2 \(\frac{2}{5},\frac{3}{5}\)
3 \(\frac{3}{5},\frac{1}{5}\)
4 \(\frac{1}{5},\frac{3}{5}\)
PHXI02:UNITS AND MEASUREMENTS

367310 The equation of state of a real gas is given by \(\left(P+\dfrac{a}{V^{2}}\right)(V-b)=R T\), where \(P, V\) and \(T\) are pressure, volume and temperature respectively and \(R\) is the universal gas constant. The dimension of \(\dfrac{a}{b^{2}}\) is similar to that of:

1 \(R T\)
2 \(P V\)
3 \(R\)
4 \(P\)
PHXI02:UNITS AND MEASUREMENTS

367311 The force ‘\(F\)’ acting on a body of density ‘\(d\)’ are related by the relation \(F = \frac{y}{{\sqrt d }}\) . The dimensions of ‘ \(y\)’ are

1 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
2 \(\left[ {{L^{ - 1}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
3 \(\left[ {{L^{ - 1}}{M^{^{\frac{3}{2}}}}{T^{ - 2}}} \right]\)
4 \(\left[ {{L^{ - \frac{1}{2}}}{M^{^{\frac{1}{2}}}}{T^{ - 2}}} \right]\)
PHXI02:UNITS AND MEASUREMENTS

367312 The velocity " \(V\) " of a particle is given in terms of time \(t\) as \(V=a t+\dfrac{b}{t+C}\).The dimensions of \(a, b, c\) are:

1 \(L^2 ; M L ; T^{-2}\)
2 \(L T^2 ; L T ; L\)
3 \(L T^{-2} ; L ; T\)
4 \(L ; L T ; T^2\)
PHXI02:UNITS AND MEASUREMENTS

367313 The potential energy of a particle varies with distance \(x\) as \(U=\dfrac{A x^{1 / 2}}{x^{2}+B}\), where \(A\) and \(B\) are constants. The dimensional formula for \(A \times B\) is

1 \(\left[M^{1} L^{7 / 2} T^{-2}\right]\)
2 \(\left[M^{1} L^{1 / 2} T^{-2}\right]\)
3 \(\left[M^{1} L^{5 / 2} T^{-2}\right]\)
4 \(\left[M^{1} L^{9 / 2} T^{-2}\right]\)
PHXI02:UNITS AND MEASUREMENTS

367314 Suppose \(A = {B^n}{C^m}\) , where \(A\) has dimensions \(LT\), \(B\) has dimensions \({L^2}{T^{ - 1}}\), and \(C\) has dimensions \(L{T^2}\). Then find the values of exponents \(n\) and \(m\) :

1 \(\frac{2}{5},\frac{4}{5}\)
2 \(\frac{2}{5},\frac{3}{5}\)
3 \(\frac{3}{5},\frac{1}{5}\)
4 \(\frac{1}{5},\frac{3}{5}\)