Motion in a Pla...

A sphere is suspended by a thread of length . What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension?

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle θ₁. In the next 2 sec, it rotates through an additional angle θ₂. The ratio of θ₂/θ₁ is

A 2 kg stone at the end of a string 1 m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m/sec. The tension in the string will be 52 N, when the stone is

A particle moves in a circle of radius 30 cm. Its linear speeds is given by v = 2t, where t in second and v in m/s. Find out its radial an tangential acceleration at t = 3sec, respectively,

The string of pendulum of length l displaced through 90^o from the vertical and released. Then, the minimum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is

A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If g = 10 m/s², then the maximum angular velocity of the stone will be

A heavy mass in attached to a thin wire and is whirled in a vertical circle. The wire id most likely to break

A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500 gm is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms^–2, then the maximum angular velocity of the stone will be

The minimum velocity at the lowest point, so that the string just slack at the highest point in a vertical circle of radius l

If the equation for the displacement of a particle moving on a circular path is given by (θ) = 2t³ + 0.5, where θ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is