Question

The dimension of force constant is

• A. \( [M^1 L T^{-2}] \)
• B. \( [M^0 L^1 T^{-2}] \)
• C. \( [M^1 L^1 T^{-2}] \)
• D. \( [M^1 L T^{-1}] \)

Hint:

To find the dimensional formula of any physical quantity, express it in terms of the fundamental quantities like mass (M), length (L), and time (T). Apply the given formula, and simplify accordingly.

Answer 1

The Correct Option is C

The force constant \( k \) in Hooke's Law, which is expressed as \( F = kx \), where \( F \) is the force and \( x \) is the displacement, has the same dimension as force per unit displacement.
- The dimension of force \( F \) is given by: \[ [F] = M L T^{-2} \] - The dimension of displacement \( x \) is: \[ [x] = L \] So, the dimension of the force constant \( k \) is: \[ [k] = \frac{[F]}{[x]} = \frac{M L T^{-2}}{L} = M L T^{-2} \] Thus, the dimension of the force constant is \( [M^1 L^1 T^{-2}] \).