Motion in a Pla...

A body is projected with a speed u m/s at an angle β with the horizontal. The kinetic energy at the highest point is 3/4 th of the initial kinetic energy. The value of β is

An object is projected so that its horizontal range R is maximum. If the maximum height attained by the object is H, then the ratio of R/H is

Two projectiles A and B thrown with speeds in the ratio 1 : √ 2 acquires the same heights. If A is thrown at an angle of 45^o with the horizontal, the angle of projection of B will be

A particle crossing the origin of coordinates at time t = 0, moves in the xy-plane with a constant acceleration a in the y - direction. If its equation of motion is y = bx² (b is a constant), its velocity component in the x-direction is

A car is moving in a circular track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is

A particle of mass m is moving in a circular path of radius r such that its centripetal acceleration a_c is varying with time t as, a_c = k²rt². The power delivered to the particle by the forces acting on it is

A stone of mass 1 kg tied to a light inextensible string of length L = 10/3 m is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m/s², the speed of the stone at the highest point of the circle is

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB (see figure) with the speed v. Friction between the bead and the string may be neglected. Let t_P and t_Q be the respective time taken by P and Q to reach the point B. Then