Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. [2026]

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Q.
Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is: [2026]

1 $\frac{2 L}{m d^{2}}$

2 $\frac{3}{2} \frac{L}{m d^{2}}$

3 $\frac{4}{3} \frac{L}{m d^{2}}$

4 $\frac{2 L}{5 m d^{2}}$

Ans.
(2)

$L = I ω and ω = \frac{L}{I}$

$ω = \frac{L}{m {(\frac{2 d}{3})}^{2} + 2 m {(\frac{d}{3})}^{2}}$ $= \frac{L}{\frac{4}{9} m d^{2} + \frac{2}{9} m d^{2}} = \frac{L}{\frac{6 m d^{2}}{9}}$

$ω = \frac{3 L}{2 m d^{2}}$

Solution

Q.
Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is: [2026]

1 $\frac{2 L}{m d^{2}}$

2 $\frac{3}{2} \frac{L}{m d^{2}}$

3 $\frac{4}{3} \frac{L}{m d^{2}}$

4 $\frac{2 L}{5 m d^{2}}$

Ans.
(2)

$L = I ω and ω = \frac{L}{I}$

$ω = \frac{L}{m {(\frac{2 d}{3})}^{2} + 2 m {(\frac{d}{3})}^{2}}$ $= \frac{L}{\frac{4}{9} m d^{2} + \frac{2}{9} m d^{2}} = \frac{L}{\frac{6 m d^{2}}{9}}$

$ω = \frac{3 L}{2 m d^{2}}$

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Solution

Q. Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is: [2026]

1 2Lmd2

2 32 Lmd2

3 43 Lmd2

4 2L5md2

Ans. (2) L=Iω and ω=LI ω=Lm(2d3)2+2m(d3)2=L49md2+29md2=L6md29 ω=3L2md2

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Q.
Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is: [2026]

1 $\frac{2 L}{m d^{2}}$

2 $\frac{3}{2} \frac{L}{m d^{2}}$

3 $\frac{4}{3} \frac{L}{m d^{2}}$

4 $\frac{2 L}{5 m d^{2}}$

Ans.
(2)

$L = I ω and ω = \frac{L}{I}$

$ω = \frac{L}{m {(\frac{2 d}{3})}^{2} + 2 m {(\frac{d}{3})}^{2}}$ $= \frac{L}{\frac{4}{9} m d^{2} + \frac{2}{9} m d^{2}} = \frac{L}{\frac{6 m d^{2}}{9}}$

$ω = \frac{3 L}{2 m d^{2}}$