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Physics · WORK, ENERGY AND POWER
हिन्दीA body of mass \( 0.5\text{ kg} \) travels along the x-axis with a velocity given by \( v(x) = a x^{3/2} \), where \( a = 5\text{ m}^{-1/2}\text{ s}^{-1} \). The work done by the net force acting on the body during its displacement from \( x = 0 \) to \( x = 2\text{ m} \) is:
Correct answer · Option 3
\( 50\text{ J} \)
Explanation
By Work-Energy theorem, \( W = \frac{1}{2} m (v_f^2 - v_i^2) \). At \( x = 0 \), \( v_i = 0 \). At \( x = 2\text{ m} \), \( v_f = 5 \times (2)^{3/2} \implies v_f^2 = 25 \times 8 = 200\text{ m}^2\text{ s}^{-2} \). Thus, \( W = \frac{1}{2}(0.5)(200) = 50\text{ J} \).
