Question

2) A spherical ball rolls on a table without slipping. Then the fraction of it's total energy associated with therotation is : a) 2/5 b)35 c)2/7 d)3/7 5) Two paricles having a charge +q and -q are connected to two rods of length l and the rod making an angle of 30degree with the electric filed direction then the coupl acting is: a)qEl b)2qEl c)qE d)2qlE

Answer 1

Moment of inertia = 2/5 M R²  of a solid sphere
Rotational energy = 1/2 I ω² = 1/5 M R² ω² = 1/5 M v² 
      as the ball is rolling,  v = R ω

 Translational energy = 1/2  M v²
Total KE = (1/2+ 1/5) M v² = 7/10 * Mv²

Fraction = 1/5  ÷ 7/10 = 2/7

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Force acting on each charge = q E
Torque due to each force = | r X F | =  q E L Sin 30 = q E L /2

Couple acting on the charges = 2 * torque =  q E L