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Please help me with this question. Answer is 0.4R. I am completely. Blank

Please help me with this question. Answer is 0.4R. I am completely. Blank

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Grade:12

1 Answers

Amrit Raj
46 Points
7 years ago
In the question frictional force vanishes when Forward velocity V=wR Where   w is angular velocity due to applied force F.
Now for calculating ,w after any time t on application of force F.We need to calculate ,∂ (angular acceleration).
By using the equation,
T(torque)=I∂          (I = Moment of inertia)
=>y.F=I∂ 
=>∂ =yF/I....................................................1
 Let at t=0,w=0
After time t,final angular velocity wf=∂t..............2
And we know that ,w=V/R................................3
On putting the values of w and ∂ from eqn 1 and 3 in eqn 2.
we get,   V/R=(yF/I.).......................................4
due to application ,of force F after time t
Vt=at =(F/M)t    …..................................5            (Assume mass of the sphere is M.)
Subtituting value of V from eqn 5 in eqn 4.
we have
(F/MR)t=(yF)/I.
=>y=0.4R       (In this case I=(2/5).MR2) so subtitute the value of I in the equation and calculate for y.
You will get, y=0.4R
        
 
 

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