A bullet of mass 10 ; g and speed 500 ; m/s i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Mass of the bullet,$m = 10 \; g = 0.01 \; kg$. Velocity of the bullet,$v = 500 \; m/s$. Width of the door,$L = 1.0 \; m$. Mass of the door,$M = 12

Vedclass · Accepted Answer

$0.625 \; rad/s$

Vedclass · Answer

(A) Mass of the bullet,$m = 10 \; g = 0.01 \; kg$. Velocity of the bullet,$v = 500 \; m/s$. Width of the door,$L = 1.0 \; m$. Mass of the door,$M = 12 \; kg$. The bullet embeds at the centre,so the distance from the hinge is $r = L/2 = 0.5 \; m$. Angular momentum of the bullet about the hinge: $L_{bullet} = mvr = 0.01 	imes 500 	imes 0.5 = 2.5 \; kg \cdot m^2/s$. Moment of inertia of the door about the hinge: $I_{door} = \frac{1}{3}ML^2 = \frac{1}{3} 	imes 12 	imes (1.0)^2 = 4 \; kg \cdot m^2$. Moment of inertia of the bullet about the hinge: $I_{bullet} = mr^2 = 0.01 	imes (0.5)^2 = 0.0025 \; kg \cdot m^2$. Total moment of inertia $I = I_{door} + I_{bullet} = 4 + 0.0025 = 4.0025 \; kg \cdot m^2$. By conservation of angular momentum,$L_{bullet} = I \omega$. $\omega = \frac{2.5}{4.0025} \approx 0.6246 \; rad/s \approx 0.625 \; rad/s$.

Similar Questions

If the radius of the Earth were to suddenly decrease,then:

Before diving into a swimming pool, a swimmer curls their body, because this

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

In the absence of torque,the rotational frequency of a body changes from $1 \text{ cy/sec}$ to $16 \text{ cy/sec}$. The ratio of the radius of gyration in the two cases will be: (in $: 1$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module