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Question

A uniform thin flat isolated disc is floating in space. It has radius R and mass m. A force F is applied to it at a distance d=r2 from the centre in the y-direction. Treat this problem as two-dimensional. Just after the force is applied :

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A
acceleration of the centre of the disc is Fm.
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B
angular acceleration of the disk is FmR.
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C
acceleration of leftmost point on the disc is zero.
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D
point which is instantaneously unaccelerated is the rightmost point.
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Solution

The correct options are
A acceleration of the centre of the disc is Fm.
B angular acceleration of the disk is FmR.
D acceleration of leftmost point on the disc is zero.
Using Newtons second law we have F=ma
or
a=Fm
Thus option A is correct.
Using torque balance we have
FR2=12mR2α
or
α=FmR
Thus option B is correct
aP=aαR=0
Now acceleration at point P
aP=aαR which equals zero.
Thus option C is also correct.
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