Motion In Two Dimensions

Two particles are separated by a horizontal distance $'x'$ as shown. They are projected at the same time as shown with different initial speeds. The time after which the horizontal distance between them becomes zero is…

Two small bodies of different masses are projected upwards with the same velocity but making angle of projection of $30^\circ$ and $60^\circ$ with the horizontal. Both these bodies will

A particle starting from rest moves along the circumference of a circle of radius $r = \sqrt{2}$ m with an angular acceleration $\alpha = \dfrac{\pi}{9}$ rad/s$^2$. The magnitude of its average velocity and…

When a bob of mass $m$ moves in a horizontal circle of radius $r$, with uniform velocity having the length of string $L$, describes a cone of semivertical angle $\theta$. The centripetal force acting on the bob is given…

A ball of mass 'm' is attached to the end of a string having length 'l'. The ball is rotated in a horizontal circle about a vertical axis. The maximum tension that a string can bear is 'T'. The maximum angular velocity…

A particle is projected at $60^\circ$ to the horizontal with kinetic energy 'K'. The kinetic energy at the highest point is $\left(\cos 60^0 = \dfrac{1}{2}\right)$

A body, performing uniform circular motion of radius 'r', has frequency 'n'. Its centripetal acceleration per unit radius is related as $(\text{n})^x$. The value of $x$ is

Two particles A and B move in concentric circles of radii $r_1$ and $r_2$ respectively in such a way that position of particles A, B and the centre of the circle (O) always lie on a straight line, the ratio of the their…

A body performs uniform circular motion with radius $\vec{r} = 4\hat{i} - 2\hat{j} + 2\hat{k}$ and angular velocity $\vec{\omega} = 2\hat{i} - 3\hat{j} + \hat{k}$. The magnitude of linear velocity of the body is

A stone of mass $100\ \text{g}$, attached at the end of a $1\ \text{m}$ long string is whirled in a horizontal circle. If the string makes an angle '$\theta$' with the vertical, then the value of centripetal force…

If two projectiles are projected with equal velocities at an angle which are complimentary to each other, then

The speed of a swimmer in still water is $20ms^{-1}.$ The speed of river water is $10ms^{-1}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle…