Mass 2m is kept on smooth circular track (R = 9 metres) of mass m which is kept on a smooth horizontal surface. The circular track is given a horizontal velocity √(2gR) towards left and released. Find the maximum height reached by 2m in metres.
Physics · Mixed Chapter
JEE Mains

Question

Mass 2m is kept on smooth circular track (R = 9 metres) of mass m which is kept on a smooth horizontal surface. The circular track is given a horizontal velocity √(2gR) towards left and released. Find the maximum height reached by 2m in metres.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Let initial speed of the track be u=√(2gR). No external horizontal force acts, so horizontal momentum stays −mu. Step 2: At the maximum height the relative motion momentarily stops, so the track and mass 2m move with the same horizontal velocity V=−u/3. Step 3: Energy conservation: ½mu²=½(3m)(u²/9)+2mgh. Hence 2mgh=mu²/3. Step 4: Using u²=2gR gives h=R/3=9/3=3 m.