Q.

Figure shows a plank of mass m moving at speed u on a smooth surface. A spinning ball (sphere) of mass m and radius r normally strikes it at speed v. The friction coefficient between ball and upper surface of plank is μ = 0.5 and coefficient of restitution is e = 0.5. Find the angular velocity of sphere just after collision.

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a

124μvr

b

154μvr

c

156μr

d

154vr

answer is B.

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Detailed Solution

As shown in figure if we write impulse = change in momentumequations  mu−J2=mv2                 mv−J1=−mv2 ⇒J1=32mv                 0+J2=mv1⇒v1=32μv=34vvelocity of ball vball=(v/2)2+(3v/4)2=134vwe also have  25mr2ω−J2r=25mr2ω125mr2ω−μ32mvr==25mr2ω1ω1=154μvr
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