JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Work, Power & Energy

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 \times 10)

Joules. The value of

n

is (take acceleration due to gravity =

10 m s^{- 2}

)

Answer: 5

Solution

Distance PQ:

P Q = O P^{2} + O Q^{2} = 9 + 16 = 5

m.

Work by applied force:

W_{F} = 18 \times 5 = 90

J.

Work by gravity: The block moves from P (height 0) to Q (height -4 m, assuming O is at P's level and Q is 4 m below).

W_{g} = m g h = 1 \times 10 \times (- 4) = - 40

J.

By work-energy theorem:

Δ K E = W_{F} + W_{g} = 90 - 40 = 50

J.

So

n \times 10 = 50

, giving

n = 5

JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Integer answer