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Physics · WORK, ENERGY AND POWER
हिन्दीA variable force \( F(x) = -cx^3 \) (where \( c = 2\text{ N m}^{-3} \)) acts on a particle of mass \( 0.25\text{ kg} \) moving along the \( x \)-axis. If the particle is released from rest at \( x = 2\text{ m} \), its speed when it passes through the origin \( x = 0 \) is:
Correct answer · Option 4
\( 8\text{ m s}^{-1} \)
Explanation
\( W = \int_{2}^{0} (-2x^3)\,dx = [-\frac{x^4}{2}]_2^0 = 0 - (-\frac{16}{2}) = 8\text{ J} \). By work-energy theorem, \( \frac{1}{2}mv^2 = 8 \implies \frac{1}{2}(0.25)v^2 = 8 \implies v^2 = 64 \implies v = 8\text{ m s}^{-1} \).
