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Physics · LAWS OF MOTION
हिन्दीA block of mass \( m = 2\text{ kg} \) is projected up a rough inclined plane of angle \( \theta = 30^\circ \) with an initial speed of \( u = 10\text{ m/s} \). The coefficient of kinetic friction between the block and the incline is \( \mu_k = \frac{1}{2\sqrt{3}} \). Taking \( g = 10\text{ m/s}^2 \), find the distance \( s \) traveled by the block up the incline before coming to instantaneous rest.
Correct answer · Option 3
\( \frac{20}{3}\text{ m} \)
Explanation
Retardation during upward motion \( a = g(\sin 30^\circ + \mu_k \cos 30^\circ) = 10 (\frac{1}{2} + \frac{1}{2\sqrt{3}} \times \frac{\sqrt{3}}{2}) = 10 (\frac{3}{4}) = 7.5\text{ m/s}^2 \). Stopping distance \( s = \frac{u^2}{2a} = \frac{100}{15} = \frac{20}{3}\text{ m} \).
