Two identical uniform discs roll without slipping on two different surfaces AB and CD starting at A and C with linear speed -1 and -2- respectively- and always remain in contact with the surfaces- If they reach B and D with the same linear speed and -1 - 3 m-s then -2 in m-s is g - 10 m-s2

K_total = K_tr + K_rot = 12mv^2 + 12Iω ^2 = 12mv^2 #160; + 12 ( mR^22)(vR)^2 =3/4mv^2 Since velocity #160; of both the discs are same a ...

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Byju's Answer

Standard XII

Physics

Pure Rolling

Two identical...

Question

Two identical uniform discs roll without slipping on two different surfaces AB and CD starting at A and C with linear speed $υ_{1}$ and $υ_{2}$ , respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and $υ_{1} = 3 m / s$ then $υ_{2}$ in m/s is $(g = 10 m / s^{2})$

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Solution

$K_{t o t a l} = K_{t r} + K_{r o t}$
$= \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$
$= \frac{1}{2} m v^{2} + \frac{1}{2} (\frac{m R^{2}}{2}) (\frac{v}{R})^{2}$
$= \frac{3}{4} m v^{2}$
Since velocity of both the discs are same at B , using conservation of energy,
$\frac{3}{4} m v_{1}^{2} + m g (30) = \frac{3}{4} m v_{2}^{2} + m g (27)$
Putting $v_{1} = 3$ and solving
$v_{2}^{2} = 49$
$\Rightarrow v_{2} = 7$

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Two identical uniform discs roll without slipping on two different surfaces $A B$ and $C D$ starting at $A$ and $C$ with linear speed $v_{1}$ 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 $(g = 10 m / s^{2})$