JEE Advance - Physics (2014 - Paper 1 Offline - No. 4)
Consider an elliptically shaped rail PQ in the vertical plane with
OP = 3 m and OQ = 4 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 PQ (see the figure given). Assuming no frictional losses, the
kinetic energy of the block when it reaches Q is (n × 10) Joules. The
value of n is (take acceleration due to gravity = 10 ms–2)
Answer
5
Explanation
Work done by the gravitational force is $${W_g} = mgh\cos 180^\circ $$
= $$-$$ mgh = $$-$$1 $$\times$$ 10 $$\times$$ 4 = $$-$$40 J
Work done by the applied force F
$${W_F} = Fd\cos 0^\circ = Fd = 18 \times 5 = 90$$ J
According to work-energy theorem
$$\Delta$$K = Wg + WF
$$\Delta$$K = $$-$$40 J + 90 J = 50 J = (5 $$\times$$ 10) J
$$\therefore$$ n = 5
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