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JEE-ADVANCED-2014
PAPER 1
Question
Consider an elliptically shaped rail PQ in the vertical plane with $\mathrm{OP}=3 \mathrm{~m}$ and $\mathrm{OQ}=4 \mathrm{~m}$. A block of mass 1 kg is pulled along the rail from $P$ to $Q$ with a force of 18 N , Which is always parallel to line $P Q$ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is ( $\mathrm{n} \times 10$ ) joules. The value of $n$ is (take acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
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Solution
$\begin{aligned} & W_f+W_g=K_f-K_1 \\ & 18 \times 5+1 g(-4)=K_t \\ & 90-40=K_t \\ & K_t=50 \mathrm{~J}=5 \times 10 \mathrm{~J}\end{aligned}$
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