A particle moves in a horizontal circle on the smooth inner surface of a hemispherical bowl of radius $R$. The plane of motion is at a depth $d$ below the centre of the hemisphere. The speed of the particle is :-
A particle moves in a horizontal circle on the smooth inner surface of a hemispherical bowl of radius $R$. The plane of motion is at a depth $d$ below the centre of the hemisphere. The speed of the particle is :-
- A
$\sqrt {\frac{{g({R^2} - {d^2})}}{R}} $
- B
$\sqrt {\frac{{g({R^2} - {d^2})}}{d}} $
- C
$\sqrt {\frac{{gR}}{{{R^2} - {d^2}}}} $
- D
$\sqrt {\frac{{g d^2}}{{{R^2} - {d^2}}}} $
Similar Questions
A cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed, the tendency to overturn is
A cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed, the tendency to overturn is
A passenger inside a bus moving with uniform speed suddenly finds that a ball at rest, starts moving towards his left. It means that the bus now is
A passenger inside a bus moving with uniform speed suddenly finds that a ball at rest, starts moving towards his left. It means that the bus now is
A string breaks if its tension exceeds $10$ newtons. A stone of mass $250\, gm$ tied to this string of length $10 \,cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be .......... $rad/s$
A string breaks if its tension exceeds $10$ newtons. A stone of mass $250\, gm$ tied to this string of length $10 \,cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be .......... $rad/s$
A vehicle is moving on a track with constant speed as shown in figure. The apparent weight of the vehicle is
A vehicle is moving on a track with constant speed as shown in figure. The apparent weight of the vehicle is
At time $t=0$, a disk of radius $1 m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} rad s ^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is. . . . . . .[Take $g=10 m s ^{-2}$.]
At time $t=0$, a disk of radius $1 m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} rad s ^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is. . . . . . .[Take $g=10 m s ^{-2}$.]
- [IIT 2022]