$\frac{1}{2} mv ^2+\frac{1}{2} I \omega^2=7 \times 10^{-3}$ $\frac{1}{2} mv ^2+\frac{1}{2}\left(\frac{2}{5} MR ^2\right)\left(\frac{ V }{ R }\right

$\frac{1}{2} mv ^2+\frac{1}{2} I \omega^2=7 \times 10^{-3}$ $\frac{1}{2} mv ^2+\frac{1}{2}\left(\frac{2}{5} MR ^2\right)\left(\frac{ V }{ R }\right)^2=7 \times 10^{-3}$ $\frac{1}{2} MV ^2\left[1+\frac{2}{5}\right]=7 \times 10^{-3}$ $\frac{1}{2}(1)\left( V ^2\right)\left(\frac{7}{5}\right)=7 \times 10^{-3}$ $V ^2=10^{-2}$ $V =10^{-1}=0.1\,m / s =10\,cm / s$

6.System of Particles and Rotational MotionMedium

A solid sphere of mass $1\,kg$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}\,J$. The speed of the centre of mass of the sphere is $.........cm s ^{-1}$.

[JEE MAIN 2023]

A
$10$
B
$9$
C
$8$
D
$7$

Std 11
Physics

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi: 22$ then, the value of its angular speed will be $...........\,rad / s$.

Medium

[JEE MAIN 2023]

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$A$ uniform rod of length $l$, hinged at the lower end is free to rotate in the vertical plane . If the rod is held vertically in the beginning and then released, the angular acceleration of the rod when it makes an angle of $45^o$ with the horizontal ($I = ml^2/3$)

Advanced

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A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\, m / s$ (as shown in figure). Maximum height with respect to the initial position covered by it will be $...........cm$.

Difficult

[JEE MAIN 2023]

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A metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $f$ rotations per second. It is suddenly stopped at $50\%$ of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is

Difficult

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Part of the tuning arrangement of a radio consists of a wheel which is acted on by two parallel constant forces as shown in the fig. If the wheel rotates just once, the work done will be about (diameter of the wheel = $0.05\ m$)

Medium

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A solid sphere of mass $1\,kg$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}\,J$. The speed of the centre of mass of the sphere is $.........cm s ^{-1}$.

Similar Questions

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi: 22$ then, the value of its angular speed will be $...........\,rad / s$.

$A$ uniform rod of length $l$, hinged at the lower end is free to rotate in the vertical plane . If the rod is held vertically in the beginning and then released, the angular acceleration of the rod when it makes an angle of $45^o$ with the horizontal ($I = ml^2/3$)

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\, m / s$ (as shown in figure). Maximum height with respect to the initial position covered by it will be $...........cm$.

A metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $f$ rotations per second. It is suddenly stopped at $50\%$ of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is

Part of the tuning arrangement of a radio consists of a wheel which is acted on by two parallel constant forces as shown in the fig. If the wheel rotates just once, the work done will be about (diameter of the wheel = $0.05\ m$)