Two equal uniform rods $P$ and $Q$ each of length $l$ move with the same velocity $v$ as shown in the figure. The second rod has an angular velocity $ω (< 6 v / l$ and clockwise) about its centre of gravity $G^{1}$ in addition to $v$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

If the ends $A$ and $A'$ are suddenly fixed simultaneously, both the rods will start to rotate with the same angular velocity.

If the ends $A$ and $A'$ are suddenly fixed simultaneously, the rod $Q$ will start to rotate with greater angular velocity.

If the ends $B$ and $B'$ are suddenly fixed simultaneously, both rods will start to rotate with the same angular velocity

If the ends $B$ and $B'$ are suddenly fixed simultaneously, the rod $P$ will start to rotate with greater angular velocity.

answer is B, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

For P : About A or B
$L_{i} = L_{f} \Rightarrow m v \frac{l}{2} = \frac{m l^{2}}{3} ω_{P} \Rightarrow ω_{P} = \frac{3 v}{2 l}$
For Q : About A
$L_{i} = L_{f} \Rightarrow m v \frac{l}{2} + \frac{m l^{2}}{12} ω = \frac{m l^{2}}{3} ω_{1} \Rightarrow ω_{1} = (\frac{v}{2} + \frac{ω l}{12}) \frac{3}{l} = \frac{3 v}{2 l} + \frac{ω}{4}$
$∴ ω_{1} > ω_{P} \Rightarrow$ Option (A) is wrong and (B) is correct.
About B
$L_{i} = L_{f} \Rightarrow ω_{2} = \frac{3 v}{2 l} - \frac{ω}{4}$
$ω_{2}$ is +ve as $ω < \frac{6 v}{l}$
$∴ ω_{2} < ω_{P} \Rightarrow$ Option (C) is wrong and (D) is correct.