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Question: Answered & Verified by Expert

A plank is moving in a horizontal direction with a constant acceleration ai^. A uniform rough cubical block of side l rests on the plank and is at rest relative to the plank.




Let the centre of mass of the block be at 0, l/2 at a given instant. If a=g/10, then the normal reaction exerted by the plank on the block at that instant acts at


PhysicsLaws of MotionKVPYKVPY 2018 (SB/SX)
Options:
  • A 0,0
  • B -l/20,0
  • C -l/10,0
  • D l/10,0
Solution:
2254 Upvotes Verified Answer
The correct answer is: -l/20,0

Given situation is



Forces acting on the block are



In above diagram,


ma= pseudo force due to acceleration of plank, f= force of static friction, mg= weight of block and N= normal reaction.


Here, we must note that due to motion of plank, normal reaction force does not passes through centre of mass.


If line of action of normal force at a distance x from centre, then for equilibrium of block, net torque about centre of mass must be zero.


τNormal reaction=τFriction


mg and ma does not produces any torque about centre of mass as their line of action passes through centre of mass.


N·x=f·l/2


mgx=mal2


N=mg & f=ma


x=agl2

or x=110·l2         a=g10


or x=l20


So, coordinates of point from which reaction passes are -l20,0


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