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  • An impulse is imparted to the solid sphere of mass 'm' and radius 'r', such that it moves up the incline plane of inclination '<img alt="\theta" src="https://entrancecorner.onco

An impulse is imparted to the solid sphere of mass 'm' and radius 'r', such that it moves up the incline plane of inclination '\theta' with a speed 'v'. If the sphere rolls without slipping on the incline plane. Then time after which the sphere will stop is given by [Given, coefficient of friction is 'g' ]

Option: 1

\frac{5 v}{2 u g \cos \theta}


Option: 2

\frac{v}{2 u g \cos \theta}


Option: 3

\frac{2}{5} \frac{v}{u g \cos \theta}


Option: 4

\frac{3}{5} \frac{v}{u g \cos \theta}


Answers (1)

best_answer

\alpha =g \sin \theta-u g \cos \theta

When sphere stops, its velocity becomes zero.v_f=0

\tau=I \alpha

\tau=f r=\frac{2 m r^2}{5} \alpha

u m g \cos \theta=\left(\frac{2 m r}{5}\right)\alpha

\alpha=\frac{5 u g \cos \theta}{2 r}

a=r \alpha=\frac{5 u g \cos \theta}{2}

\Rightarrow t=\frac{2 v}{5 u g \cos \theta}

Posted by

Pankaj

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