Q103 / 200 · NEET 2023 (Manipur) · Physics

The mechanical quantity, which has dimensions of reciprocal of mass $\left(\mathrm{M}^{-1}\right)$ is

  • A
    Torque
  • Correct answer
    B
    Gravitational constant
  • C
    Angular momentum
  • D
    Coefficient of thermal conductivity

Solution

We know that, $F=\frac{G M_1 M_2}{r^2}$ $\begin{aligned} & \Rightarrow \quad[G]=\frac{[F]\left[r^2\right]}{\left[M_1\right]\left[M_2\right]}=\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^2\right]}{[\mathrm{M}][\mathrm{M}]} \\ & \Rightarrow[G]=\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\end{aligned}$ i.e., gravitational constant is mechanical quantity which has dimensions of reciprocal of mass $\left(\mathrm{M}^{-1}\right)$

Hence, the correct answer is option: 'B'.

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