A small cube with mass M starts at rest at point 1 at a height 4R , where R is radius of circular pa

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5.Work, Energy, Power and Collision

hard

$A$ small cube with mass $M$ starts at rest at point $1$ at a height $4R$, where $R$ is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point $2$ is nearly ......... times the cube's weight $mg$.

A

$1$

B

$2$

C

$3$

D

$4$

Solution

velocity at bottom most point $=\sqrt{8} g r$

Now, at $2$ its displacement from bottom most point is $2 R$ The velocity at $2$ will be$:-$

$v^{2}=u^{2}+2 a s$

$v^{2}=8 g R+2(-g)(2 R)$

$v^{2}=4 g R$

Now, net force at $2=F+m g=\frac{m v^{2}}{R}$

$F=\frac{m(4 g R)}{R}-m g f=3 m g$

Standard 11

Physics

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