Question

A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On applying brakes, the stopping distance is \( S_1 \). The man returns home on the same scooter, with the same speed, with a 60 kg bag of rice. If \( S_2 \) is the new stopping distance when the brakes are applied with the same force, then:

• A. \( 7S_1 = 4S_2 \)
• B. \( 2S_1 = S_2 \)
• C. \( 3S_1 = 4S_2 \)
• D. \( 4S_1 = 3S_2 \)

Hint:

Stopping distance is proportional to mass when force is constant. - Use energy conservation to find stopping distance.

Answer 1

The Correct Option is D

Step 1: Use work-energy theorem
The work done by braking force \( F \) is: \[ W = F S. \] Since work done equals the initial kinetic energy, \[ \frac{1}{2} m v^2 = F S. \] Step 2: Compute ratio of stopping distances
For initial mass \( M_1 = 80 + 100 = 180 \) kg, \[ S_1 \propto \frac{M_1}{F}. \] For new mass \( M_2 = 180 + 60 = 240 \) kg, \[ S_2 \propto \frac{M_2}{F}. \] \[ \frac{S_1}{S_2} = \frac{180}{240} = \frac{3}{4}. \] \[ 4S_1 = 3S_2. \] Thus, the correct answer is \( \boxed{4S_1 = 3S_2} \).