Dimensional Analysis – Rankers Physics

Dimensions: Practice Problem & Solution

The mechanical quantity, which has dimensions of reciprocal of mass \( \text{M}^{-1} \) is
Torque
Gravitational constant
Angular momentum
Coefficient of thermal conductivity

Solution Explained:

To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:

The dimension of the universal gravitational constant \(G\) is \([\text{M}^{-1}\text{L}^3\text{T}^{-2}]\). Therefore, its dimensions contain the reciprocal of mass.

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): The dimensions of base (fundamental) quantity in other base quantities is always zero. Reason (R): All derived quantities may be represented dimensionally in terms of fundamental quantities.  
2. Assertion (A): A displacement can be added with a distance. Reason (R): Adding a scalar to a vector of the same dimensions is a meaningful algebraic operation.  
3. Dimensional formula for torque is
4. Assertion (A): When an algebraic equation has been derived, it is advisable to check it for dimensional consistency. Reason (R): This guarantees that the equation is correct.  
5. Match the column:\n(a) Pressure -> (i) \([ML^2T^{-1}]\)\n(b) Angular Momentum -> (ii) \([M^{-1}L^{-3}T^4A^2]\)\n(c) Magnetic Field -> (iii) \([MT^{-2}A^{-1}]\)\n(d) Permittivity of free space -> (iv) \([ML^{-1}T^{-2}]\)\n(v) \([MT^{-2}A^{-1}]\)