Laws of Motion ...

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance $$L$$ from one end of the rod. The rod is set in angular motion about a vertical axis passing through A with a constant angular acceleration $$\alpha $$. The friction coefficient between the rod and the bead is $$\mu $$.Neglecting gravity, what is the time after which the bead starts slipping on the rod.

A mass of $$6\ kg$$ is suspended by a rope of length $$2\ m$$ from a ceiling. A force of $$50\ N$$ is applied in horizontal direction at the mid point of the rope. What is the angle between the rope and the vertical in equilibrium.

Four point charges are placed in a straight line with magnitude and separation as shown in the diagram. What should be the value of $${q_0}$$ such that $$ + 10\mu C\;ch\arg e$$ is in equlibrium?

For a paticle in a vertically circle with unifrom speed, the maximum and minimum tension in the string are in the ratio 5 : 3, if the radius of vertical circle is 2 m, the speed of revolving body is $$ ( g= 10 m/s^2) $$

A road is banked at an angle of $$37^{ 0 }.$$ If a car moving at 54 km/hr does not experience any friction force while negotiating the curve, the radius of curve is :-

A mass is performing circular motion in a vertical plane centered at $$O$$. The average velocity of the particle is in creased, then at which point the string will break:

A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown. Relative to its initial position with respect to the table, the ball
I. Remains stationary if there is no friction between the paper and the ball.
II. Moves to the left and starts rolling backwards, i.e. to the left if there is a friction between the paper and the ball.
III. Moves forward, i.e., in the direction in which the paper is pulled.
Here, the correct statements is/ are

Force applied on a body is given by $$ F = (3t^2 - 2t + 10) N$$ where t is in seconds. Find impulse in t = 0 to t = 2 sec.

A body of mass $$M$$ hits normally a rigid wall with velocity $$V$$ and bounces back with the same velocity. The impulse experienced by the body is

A cyclist riding the bicycle at a speed of $$ \sqrt { 3 } m/s $$ takes a turn around a circular road of radius $$ 20 \sqrt { 3 } m $$ without skidding. What is his inclination to the vertical?