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  4. A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m / s at t=0 s on a rough horizontal surface. It starts off with a purely sliding motion at t=0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be J (given, coefficient of friction is 0.3 and .g =10 m / s 2).

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Q. A uniform disc of mass $0.5\, kg$ and radius $r$ is projected with velocity $18 \,m / s$ at $t=0$ s on a rough horizontal surface. It starts off with a purely sliding motion at $t=0\, s$. After $2\, s$ it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after $2 \,s$ will be ______ $J$
(given, coefficient of friction is $0.3$ and $\left.g =10\, m / s ^2\right)$.Physics Question Image

JEE MainJEE Main 2023System of Particles and Rotational Motion

Solution:

$a =-\mu_{ k } g =-3 $
$ V =18-3 \times 2 $
$ V =12\, m / s $
$ KE =\frac{1}{2} mv ^2+\frac{1}{2} \frac{ mr ^2}{2} \frac{ v ^2}{ r ^2}$
$KE =\frac{3}{4} mv ^2$
$ KE =3 \times 18=54\, J $