Rotational Dynamics | JEE Main previous year questions with Solutions

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Topic Question Set

Q 1 :

A uniform bar of length 12 cm and mass 20m lies on a smooth horizontal table. Two point masses m and 2m are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $ω .$ The ratio of v and $ω$ is : [2026]

$2 \sqrt{88}$
33
66
32

1

2

3

4

(2)

Using angular momentum conservation about COM of rod:

$L_{i} = L_{f}$

$m \times V \times 4 + 2 m \times V \times 2 = (\frac{20 m {(12)}^{2}}{12} + m \times 4^{2} + 2 m \times 2^{2}) ω$

$8 m V = (240 m + 24 m) ω$

$8 V = 264 ω$

$\frac{V}{ω} = 33$

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