A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m which applying the force and the ball goes upto 2 m height further, find the magnitude of the force. Consider
- (A)22 N✓ Correct
- (B)4 N
- (C)16 N
- (D)20 N
Answer: (A)
Solution
The ball rises 0.2 m while the hand pushes and then 2 m further in free flight, so it reaches 0.2 + 2 = 2.2 m above the start and is momentarily at rest at the top. Because it starts and ends at rest, the work done by the hand equals the total gain in gravitational PE: F·(0.2) = mg·(2.2) = 0.2×10×2.2 = 4.4 J, so F = 22 N → option A. (Check via the push phase: F·s − mg·s = ½mv² with v² = 2g·2 = 40, giving 0.2F − 0.4 = 4, F = 22 N.) The source's 20 N wrongly drops the 0.2 m push height from the PE balance.
JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option