A particle of mass m is projected at 45^o at V_0 speed from point P at t = 0 . angular momnetum of p

English

Gujarati

Hindi

6.System of Particles and Rotational Motion

hard

A particle of mass $m$ is projected at $45^o$ at $V_0$ speed from point $P$ at $t = 0$. The angular momnetum of particle about $P$ at $t = \frac{V_0}{g}$ is:-

A

$\frac{1}{2 \sqrt 2} \frac{mV_0^3}{g}$

B

$\frac{1}{2 \sqrt 2} \frac{mV_0^2}{g}$

C

$\frac{1}{2} \frac{mV_0^3}{g}$

D

$\frac{1}{2} \frac{mV_0^2}{g}$

Solution

$\tau=\operatorname{mg} \mathrm{x}=$ torque

$\tau=\operatorname{mg}\left(V_{0} \cos 45\right) t$

$\frac{d J}{d t}=\frac{m g V_{0}}{\sqrt{2}} t$

$\int_{0}^{\mathrm{J}} \mathrm{d} \mathrm{J}=\int_{0}^{\mathrm{t}} \frac{\mathrm{mg} \mathrm{V}_{0}}{\sqrt{2}} \mathrm{t} \mathrm{dt}$

$J=\frac{m g V_{0}}{\sqrt{2}} \frac{t^{2}}{2}$

$J=\frac{m g V_{0}^{3}}{2 \sqrt{2} g^{2}}$

$J=\frac{1}{2 \sqrt{2}} \frac{m V_{0}^{3}}{g}$

Standard 11

Physics

Share

Similar Questions

A disc of mass $M$ and radius $R$ is rolling with angular speed $\omega $ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $O$ is

medium

A thin rod of mass $M$ and length $a$ is free to rotate in horizontal plane about a fixed vertical axis passing through point $O$. A thin circular disc of mass $M$ and of radius $a / 4$ is pivoted on this rod with its center at a distance $a / 4$ from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity $\Omega$ and the disc rotating about its vertical axis with angular velocity $4 \Omega$. The total angular momentum of the system about the point $O$ is $\left(\frac{ M a^2 \Omega}{48}\right) n$. The value of $n$ is. . . . .

medium

(IIT-2021)

Explain Angular momentum of a particle and show that it is the moment of linear momentum about the reference point.

medium

$A$ paritcle falls freely near the surface of the earth. Consider $a$ fixed point $O$ (not vertically below the particle) on the ground.

hard

$A$ uniform rod is fixed to a rotating turntable so that its lower end is on the axis of the turntable and it makes an angle of $20^o$ to the vertical. (The rod is thus rotating with uniform angular velocity about a vertical axis passing through one end.) If the turntable is rotating clockwise as seen from above. What is the direction of the rod's angular momentum vector (calculated about its lower end)?

hard