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…

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…

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 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

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…

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…

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…

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…

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

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 particle is projected at an angle of $30^{\circ}$ with the horizontal with a momentum $p$. At the highest point its momentum is