Question

# A solid sphere and sperical shell of same mass m and same radius R are given charges +Q and -Q. Both spheres are kept on rough surface where friction is sufficient to avoid sliding. Initial seperation between spheres is 10 R. If m = 126 kg, Q2=23×10−9C2 and R = 1m. (A) Speed of solid sphere just before collision is 1) 35 m/s (B) Speed of spherical shell just before collision is 2) 0 m/s2 (C) Speed of center of mass just before collision is 3) 57 m/s (D) Acceleration of center of mass 4) Towards left 5) Towards right

A
A 3, B 1, 4, C 5, D 5
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B
A 1, B 3, 4, C 4, D 5
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C
A 1, B 1, 4, C 5, D 4
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D
A 3, B 3, 4, C 4, D 4
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Solution

## The correct option is A A → 3, B → 1, 4, C → 5, D → 5 By conservation of energy. −kQ210R=−kQ22R+12IAω2A+12IAω2B ---(1) IA=75 mR2 and IB=53mR2 are MOI about IAOR. By conservation of angular momentum about any point on surface ⇒ IAωA=IBωB ⇒ 75mR2ωA=53mR2ωB ---(2) Solving (1) and (2) we get ωA=2521ωB and and ω2B=21×625×23 9×109Q2mR3 ⇒ ωB=35rad/s and vB=RωB=35m/s also ωA=57rad/s and vA=57m/s Since fB>fA acceleration of COM is towards right.

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