A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10-3 J. The speed of the centre of mass of the sphere is cm s -1

Question

A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10-3 J. The speed of the centre of mass of the sphere is cm s -1 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(1/2) mv 2+(1/2) I ω2=7 × 10-3 (1/2) mv 2+(1/2)((2/5) MR 2)(( V / R ))2=7 × 10-3 (1/2) MV 2[1+(2/5)]=7 × 10-3 (1/2)(1)( V 2)((7/5))=7 × 10-3 V 2=10-2 V =10-1=0.1 m / s =10 cm / s

Q. A solid sphere of mass 1kg rolls without slipping on a plane surface. Its kinetic energy is 7×10−3J. The speed of the centre of mass of the sphere is ___cms−1

21​mv2+21​Iω2=7×10−3 21​mv2+21​(52​MR2)(RV​)2=7×10−3 21​MV2[1+52​]=7×10−3 21​(1)(V2)(57​)=7×10−3 V2=10−2 V=10−1=0.1m/s=10cm/s

Q. A solid sphere of mass $1 k g$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 1 0^{- 3} J$ . The speed of the centre of mass of the sphere is ___ $c m s^{- 1}$