Motion in a Pla...

A particle moves with an initial velocity u and retardation a v, where v is the velocity at any time t.

A particle moving along a straight line with uniform acceleration has velocities 7 ms^–1 at A and 17 /ms at B. C is the mid point of AB. Then

two particles A and B are projected with same speed so that ratio of their maximum heights reached is 3:1. If the speed of A is doubles without altering other parameters, the ratio of the horizontal ranges attained by A and B is

A particle of mass m is projected from the ground with an initial speed u₀ at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u₀. The angle that the composite system makes with the horizontal immediatley after the collision is

Two racing cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is mv²/r and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is

if the length of the second\'s hand in a stop clock is 3 cm, the angular velocity and linear velocity of the tip is

What is the angular velocity of Earth?

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel?