Consider a body, shown in figure, consisting of two identical balls, each of mass $M$ connected by a light rigid rod. If an impulse $J = M V$ is imparted to the body at one of its ends, what would be its angular velocity [2003]

Question

Smart Achievers · Accepted Answer

(1)

Applying change in angular momentum of the system = angular impulse given to the system about the centre of mass

${(Angular momentum)}_{f} - {(Angular momentum)}_{i}$

$= M v \times \frac{L}{2} = I_{C} ω . . . (i)$

Here $ω$ is the angular velocity of the rod.

Moment of Inertia of the system about its axis of rotation [centre of mass of the system]

$I_{C} = M {(\frac{L}{2})}^{2} + M {(\frac{L}{2})}^{2} = \frac{2 M L^{2}}{4} = \frac{M L^{2}}{2}$

$∴$ $\frac{M V L}{2} = (\frac{M L^{2}}{2}) ω \Rightarrow ω = \frac{V}{L}$

Solution

Q.
Consider a body, shown in figure, consisting of two identical balls, each of mass $M$ connected by a light rigid rod. If an impulse $J = M V$ is imparted to the body at one of its ends, what would be its angular velocity [2003]

1 $\frac{V}{L}$

2 $\frac{2 V}{L}$

3 $\frac{V}{3 L}$

4 $\frac{V}{4 L}$

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Solution

Q. Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity [2003]

1 VL

2 2VL

3 V3L