A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m / s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad / s ) of the rod immediately after the collision will be .

Question

A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m / s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad / s ) of the rod immediately after the collision will be . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/415f99ad73aad17c4654954830af50d0-.png" /> vec L i = vec L f mvL = I ω mvL =(( ML 2/3)+ mL 2) ω 0.1 × 80 × 1=((0.9 × 12/3)+0.1 × 12) ω 8=((3/10)+(1/10)) ω=(4/10) ω ω=20 rad ( rad / sec )

Li​=Lf​ mvL=Iω mvL=(3ML2​+mL2)ω 0.1×80×1=(30.9×12​+0.1×12)ω 8=(103​+101​)ω=104​ω ω=20radsecrad​

$L_{i} = L_{f}$
$m vL = I ω$
$m vL = (\frac{M L ^{2}}{3} + m L^{2}) ω$
$0.1 \times 80 \times 1 = (\frac{0.9 \times 1 ^{2}}{3} + 0.1 \times 1^{2}) ω$
$8 = (\frac{3}{10} + \frac{1}{10}) ω = \frac{4}{10} ω$
$ω = 20 r a d \frac{r a d}{sec}$