A cube of mass starts at rest from point at a height , where radius of the circular track. The cube slides down the frictionless track and around the loop. The force which the track exerts on the cube at point is:
A
3mg
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B
mg
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C
2mg
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D
cubewillnotreachthepoint2
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Solution
The correct option is A3mg Applying Conservation of Energy:
Total mechanical energy at 1= Total mechanical energy at 2
⇒K1+P1=K2+P2
⇒0+mg(4R)=12mv2+mg(2R) (Taking ground as reference)
⇒12v2=2gR
⇒v=√4gR→(1)
Now forces acting on block at point 2 from it's own frame are:
1. Normal(N) due to track downward
2. weight(mg) downward
3. Centrifugal force (mv2R) upward
For vertical equilibrium:
N+mg=mv2R
⇒N=m4gRR−mg (Using equation 1)
⇒N=4mg−mg=3mg
So force exerted by track on block at point 2 is 3mg