Question

The figure below shows the top view of a hollow cylindrical room having a frictionless floor. A block of mass $m$ is projected with a speed $v$ , on the smooth horizontal floor, along the wall of the room. The average normal force exerted by the cylindrical walls, on the block, during its motion from $A$ to $B$ is

• A. $\frac{m v^{2}}{R}$
• B. $\frac{m v^{2}}{\pi R}$
• C. $\frac{2 m v^{2}}{R}$
• D. $\frac{2 m v^{2}}{\pi R}$

Answer 1

Answer: (D)

The change in momentum of the block from $A$ to $B$ is
$\left|\Delta p\right|=2mv$
The time it takes to move from $A$ to $B$ is
$\Delta t=\frac{\pi R}{v}$
The average force exerted by the wall on the block is
$F_{avg}=\frac{\left|\Delta p\right|}{\Delta t}=\frac{2 m v^{2}}{\pi R}$