Q. A hoop of radius $r$ weights $m\, kg$. It rolls without sliding along a horizontal floor so that its centre of mass has a speed $v \,m / s$. How much work has to be done to stop it?

System of Particles and Rotational Motion Report Error

A

$\frac{1}{2} m v^{2}$

100%

B

$m v^{2}$

0%

C

$2 m v^{2}$

0%

D

$\frac{1}{3} m v^{2}$

0%

Solution:

Total kinetic energy of hoop is
$K=\frac{1}{2} I \omega^{2}+\frac{1}{2} m v^{2}$
$\Rightarrow K=\frac{1}{2} m r^{2} \cdot \frac{v^{2}}{r^{2}}+\frac{1}{2} m v^{2}$
$\Rightarrow K=\frac{1}{2} m v^{2}+\frac{1}{2} m v^{2}$
$\Rightarrow K=m v^{2}$
Thus, a work of $m v^{2}$ has to be done to stop it.

Questions from System of Particles and Rotational Motion

1. A disc is rolling, the velocity of its centre of mass is $V_{cm}$. Which one of these will be correct ?

AIPMT 2001

2. The centre of mass of a system of three particles of masses $1\,g, 2\,g$ and $3\,g$ is taken as the origin of a coordinate system. The position vector of a fourth particle of mass $4\, g$ such that the centre of mass of the four particle system lies at the point $(1, 2, 3)$ is a $(\hat i + 2 \hat j + 3 \hat k)$ , where a is a constant. The value of $\alpha$ is

3. Two particles of equal mass have velocities $\vec{\upsilon_{1}}=4\hat{i}\,m\,s^{-1}$ and $\vec{\upsilon_{2}}=4\hat{j}\,m\,s^{-1}$. First particles has an acceleration $\vec{a}_{1}=\left(5\hat{i}+5\hat{j}\right)m\,s^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

4. What is the torque of a force $ 3\hat{i}+7\hat{j}+4\hat{k} $ about the origin, if the force acts on a particle whose position vector is $ 2\hat{i}+2\hat{j}+1\hat{k} $ ?

J & K CET 2014

5. The angular velocity of a body is $\overset{ \rightarrow }{\omega }=2\hat{i}+3\hat{j}+4\hat{k}$ and a torque $\overset{ \rightarrow }{\tau}=\hat{i}+2\hat{j}+3\hat{k}$ acts on it. The rotational power will be

NTA Abhyas 2020

Physics Most Viewed Questions

1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

NEET 2021 Physical World, Units and Measurements

2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

NEET 2020 Dual Nature of Radiation and Matter

3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

NEET 2021 Motion in a Straight Line

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

NEET 2020 Electromagnetic Induction

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$

NEET 2020 Mechanical Properties of Fluids