Question

The masses of blocks \(A\) and \(B\) are \(m\) and \(M\) respectively. Between \(A\) and \(B\) there is a constant frictional force \(F\). Block \(B\) can slide on a smooth horizontal surface. \(A\) is set in motion with velocity \(v_0\) while \(B\) is at rest. What is the distance moved by \(A\) relative to \(B\) before they move with the same velocity? 

• A. \(\dfrac{mMv_0^2}{F(m-M)}\)
• B. \(\dfrac{mMv_0^2}{2F(m-M)}\)
• C. \(\dfrac{mMv_0^2}{F(m+M)}\)
• D. \(\dfrac{mMv_0^2}{2F(m+M)}\)

Hint:

For friction between blocks: \[ a_{\text{rel}} = a_1 - a_2 \] Always use relative motion equations.

Answer 1

The Correct Option is D