Consider a uniform rod of mass M = 4m and length l pivoted about its centre. A mass m moving with velocity ν making angle θ = (π/4) to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :

Question

Consider a uniform rod of mass M = 4m and length l pivoted about its centre. A mass m moving with velocity ν making angle θ = (π/4) to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is : (A) (4/7) (ν/l) (B) (3√2/7) (ν/l) (C) (3/7√2) (ν/l) (D) (3/7) (ν/l)

Tardigrade Admin · Accepted Answer

Let angular velocity of the system after collision be ω. By conservation of angular momentum about the hinge: m((v/√2))((ℓ/2))=[(4mℓ2/12)+(mℓ2/4)]ω On solving ω=(3√2/7)((v/ℓ))

Q. Consider a uniform rod of mass $M = 4 m$ and length $l$ pivoted about its centre. A mass $m$ moving with velocity $ν$ making angle $θ = \frac{π}{4}$ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :

$\frac{4}{7} \frac{ν}{l}$

$\frac{3 2}{7} \frac{ν}{l}$

$\frac{3}{7 2} \frac{ν}{l}$

$\frac{3}{7} \frac{ν}{l}$

Let angular velocity of the system after collision be $ω$ .
By conservation of angular momentum about the hinge :
$m (\frac{v}{2}) (\frac{ℓ}{2}) = [\frac{4 m ℓ ^{2}}{12} + \frac{m ℓ ^{2}}{4}] ω$
On solving
$ω = \frac{3 2}{7} (\frac{v}{ℓ})$

Q. Consider a uniform rod of mass M=4m and length l pivoted about its centre. A mass m moving with velocity ν making angle θ=4π​ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :

74​lν​

732​​lν​

72​3​lν​

73​lν​