A heavy spherical ball is constrained in a frame as shown in figure. The inclined surface is smooth. The maximum acceleration with which the frame can move without causing the ball to leave the frame is 2n/√3. Find value of n. [Take g = 10m/s²]
Physics · Mixed Chapter
JEE Mains

Question

A heavy spherical ball is constrained in a frame as shown in figure. The inclined surface is smooth. The maximum acceleration with which the frame can move without causing the ball to leave the frame is 2n/√3. Find value of n. [Take g = 10m/s²]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: In the accelerating frame of the support, a leftward pseudo force ma acts on the ball, together with downward weight mg. The smooth inclined face is at 30° to the horizontal. Step 2: The ball just loses contact with the right wall when that wall's reaction becomes zero. Then only the inclined-plane normal N balances mg and pseudo force. Step 3: The inclined-plane normal makes 30° with the vertical, so tan30°=(ma)/(mg), giving a=g tan30°=10/√3 m s⁻². Step 4: This equals 2n/√3, so 2n=10 a…