Comprehension Type: A uniform thin cylindrical disk of mass M ad radius R is attached to two identical mass less springs of springs constant k which are fixed to the wall as show in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its center. The axle is mass less and both the springs and the axle are in horizontal plane. The un-stretched length of each springs is L. The disk is initially at its equilibrium position with its center of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity →(V)0=V0^i The coefficient of friction is μ.
The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is
Comprehension Type: A uniform thin cylindrical disk of mass M ad radius R is attached to two identical mass less springs of springs constant k which are fixed to the wall as show in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its center. The axle is mass less and both the springs and the axle are in horizontal plane. The un-stretched length of each springs is L. The disk is initially at its equilibrium position with its center of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity →(V)0=V0^i The coefficient of friction is μ.
The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is
The correct option is D −4kx3
Net force at any x will be : f - 2kx
f - 2kx = Ma, fR = - Iα⇒fR=−(12)MR2(aR) solve to get net force
=Ma=−4kx3
Negative sign is because this force will act in backward direction.
−4kx3
Net force at any x will be : f - 2kx
f - 2kx = Ma, fR = - Iα⇒fR=−(12)MR2(aR) solve to get net force
=Ma=−4kx3
Negative sign is because this force will act in backward direction.
