Work Energy Power

JEE Main level, single correct, medium

129 of 183

Question 129 of 183

A small ball of mass m\mathrm{m} starts at a point A\mathrm{A} with speed vo\mathrm{v}_{\mathrm{o}} and moves along a frictionless track AB\mathrm{AB} as shown. The track BC\mathrm{BC} has coefficient of friction μ\mu. The ball comes to stop at C\mathrm{C} after travelling a distance LL which is:

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Answer: (B) hμ+v022μg\frac{\mathrm{h}}{\mu}+\frac{\mathrm{v}_0^2}{2 \mu \mathrm{g}}

Initial speed at point A, u=v0u=v_0
Speed at point B,v=\mathrm{B}, v= ?
v2−u2=2ghv2=v02+2gh\begin{aligned} &v^2-u^2=2 g h \\ &v^2=v_0^2+2 g h \end{aligned}
Let ball travels distance ' SS ' before coming to rest
S=v22μg=v02+2gh2μg=v022μg+2gh2μg=hμ+v022μg\begin{aligned} &S=\frac{v^2}{2 \mu g}=\frac{v_0^2+2 g h}{2 \mu g} \\ &=\frac{v_0^2}{2 \mu g}+\frac{2 g h}{2 \mu g}=\frac{h}{\mu}+\frac{v_0^2}{2 \mu g} \end{aligned}

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