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  • A solid sphere of mass '  ' and radius ' <img alt="1 \mathrm{~m}" src="ht

A solid sphere of mass ' 2 \mathrm{~kg} ' and radius ' 1 \mathrm{~m} ' is placed on a sufficiently rough horizontal surface as shown in the figure. A force having '10 N' magnitude is applied at a height of 1.8 \mathrm{~m} from the point of contact. Find the velocity of the centre of mass at t=10 \mathrm{~s}.

Option: 1

1.28 \mathrm{~m/s}


Option: 2

0.64 \mathrm{~m/s}


Option: 3

9.0 \mathrm{~m/s}


Option: 4

6.4 \mathrm{~m/s}


Answers (1)

best_answer

Taking angular impulse about point O

\begin{aligned} & \text { Angular impulse }= \text { Change in angular momentum } & \begin{aligned} \end{aligned} \\ & 1.8 \times 10= 2 \times 1 \times v_{c \cdot m}+\frac{2}{5} \times 2 \times 1^2 \times v_{c \cdot m} \\ & 18= 2 v_{c \cdot m}+\frac{4}{5} v_{c \cdot m} \\ & 18= \frac{14}{5} v_{c \cdot m} \\ & v_{c \cdot m}=\frac{18\times5}{14}=\frac{45}{7}=6.4 \mathrm{~m} / \mathrm{s} \end{aligned}

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Ajit Kumar Dubey

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