Two identical uniform discs roll without slipping on two differen… - Vidyadip

MCQ

Two identical uniform discs roll without slipping on two different surfaces $AB$ and $CD$ (see figure) starting at $A$ and $C$ with linear speeds $v _1$ and $v _2$, respectively, and always remain in contact with the surfaces. If they reach $B$ and $D$ with the same linear speed and $v_1=3 \ m / s$, then $v_2$ in $m / s$ is $\left(g=10 \ m / s ^2\right)$

A
$5$
B
$6$
✓
$7$
D
$8$

✓

Answer

Correct option: C.

$7$

c
Kinetic energy of a pure rolling disc having velocity of centre of mass $v=\frac{1}{2} m v^2+\frac{1}{2}\left(\frac{m R^2}{2}\right) \frac{v^2}{R^2}=\frac{3}{4} m v^2$

So, $\frac{3}{4} m(3)^2+m g(30)=\frac{3}{4} m\left(v_2\right)^2+m g(27) \quad \therefore v_2=7 m / s$

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