Verified Solution • 2025–26 Session moderate

QJEEM23Phf3bf: JEE Main 2023 Physics - Class 11 JEEM23Phf3bf Solution: A solid sphere of mass 1   kg rolls without slipping on a…

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

Step-by-Step Verified Solution

12mv2+12Iω2=7×10−3\frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2} \mathrm{I} \omega^{2}=7 \times 10^{-3}

⇒ 12mv2+12(25MR2)(VR)2=7×10−3\frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2}\left(\frac{2}{5} \mathrm{MR}^{2}\right)\left(\frac{\mathrm{V}}{\mathrm{R}}\right)^{2}=7 \times 10^{-3}

⇒ 12MV2[1+25]=7×10−3\frac{1}{2} \mathrm{MV}^{2}\left[1+\frac{2}{5}\right]=7 \times 10^{-3}

⇒ 12(1)(V2)(75)=7×10−3\frac{1}{2}(1)\left(\mathrm{V}^{2}\right)\left(\frac{7}{5}\right)=7 \times 10^{-3}

⇒ V2=10−2\mathrm{V}^{2}=10^{-2}

⇒ V=10−1=0.1 m/s=10 cm/s\mathrm{V}=10^{-1}=0.1 \mathrm{~m} / \mathrm{s}=10 \mathrm{~cm} / \mathrm{s}

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