Question

A car C of mass m₁ rests on a plank P of mass m₂. The plank rests on a smooth floor. The string and pulley are ideal. The car starts and moves towards the pulley with acceleration.

(a) If m₁ > m₂, the string will remain under tension. 

(b) If m₁ < m₂, the string will become slack. 

(c) If m₁ = m₂, the string will have no tension, and C and P will have accelerations of equal magnitude. 

(d) C and P will have accelerations of equal magnitude if m₁ ≥ m₂.

Answer 1

Correct Answer is: (a, b, c, & d)

Let T = tension in the string,

F = force of friction between C and P.

If the string is under tension, the acceleration of C to the right = acceleration of P to the left = a.

T + F = m₁a F - T = m₂a

∴ T = 1/ 2 (m₁ - m₂) a or T > 0 if m₁ > m₂.

If m₁ < m₂, T becomes < 0, i.e., it becomes slack.

If m₁ = m₂, T = 0.