A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass $K$. If radius of the ball be $R$, then the fraction of total energy associated with its rotational energy will be
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass $K$. If radius of the ball be $R$, then the fraction of total energy associated with its rotational energy will be
- [AIPMT 2003]
- A
$\frac{{{K^2}}}{{{R^2}}}$
- B
$\frac{{{K^2}}}{{{K^2} + {R^2}}}$
- C
$\frac{{{R^2}}}{{{K^2} + {R^2}}}$
- D
$\frac{{{K^2} + {R^2}}}{{{R^2}}}$
Similar Questions
A rod of length $l$ is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in the vertical position is
A rod of length $l$ is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in the vertical position is
Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $P$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum, is given by
Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $P$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum, is given by
- [AIPMT 2015]
A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reaches upto maximum heights $h_1$ and $h_2$, respectively, above the initial level. The ratio $h_1: h_2$ is $\frac{n}{10}$. The value of $\mathrm{n}$ is__________.
A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reaches upto maximum heights $h_1$ and $h_2$, respectively, above the initial level. The ratio $h_1: h_2$ is $\frac{n}{10}$. The value of $\mathrm{n}$ is__________.
- [JEE MAIN 2024]
A student of mass $M$ is $1.5 \,m$ tall and has her centre of mass $1 \,m$ above ground when standing straight. She wants to jump up vertically. To do so. she bends her knees so that her centre of mass is lowered by $0.2 \,m$ and then pushes the ground by a constant force F. As a result, she jumps up such that the maximum height of her feet is $0.3 \,m$ above ground. The ratio $F / Mg$ is
A student of mass $M$ is $1.5 \,m$ tall and has her centre of mass $1 \,m$ above ground when standing straight. She wants to jump up vertically. To do so. she bends her knees so that her centre of mass is lowered by $0.2 \,m$ and then pushes the ground by a constant force F. As a result, she jumps up such that the maximum height of her feet is $0.3 \,m$ above ground. The ratio $F / Mg$ is
- [KVPY 2021]
A flywheel is in the form of solid circular disc of mass $72\,\, kg$ and radius of $0.5\,m$ and it takes $70\, r.p.m.$ , then the energy of revolution approximately is ....... $J.$
A flywheel is in the form of solid circular disc of mass $72\,\, kg$ and radius of $0.5\,m$ and it takes $70\, r.p.m.$ , then the energy of revolution approximately is ....... $J.$