Laws of Motion ...

A simple pendulum with bob of mass $$m$$ and length $$x$$ is held in position at an angle $$1$$ and then angle $$2$$ with the vertical. When released from these positions, speeds with which it passes the lowest positions are $${v}_{1}$$ and $${v}_{2}$$ respectively. Then, $$\cfrac { { v }_{ 1 } }{ { v }_{ 2 } } $$ is 

A curved road of diameter $$1.8\ km$$ is banked so that no friction is required at a speed of $$30\ m/s$$. What is the banking angle?

A particle of mass m strikes a wall with speed v at an angle $$30^0$$ with the wall elastically as shown in the figure. The magnitude of impulse imparted to the ball by the wall is :

A bullet is fired from a gun. The force on the bullet is given by $$F = 600 - 2\times 10^{5}t$$, where $$F$$ is in newtons and $$t$$ in seconds. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

If n balls hit elastically and normally on a surface per unit area and all units has mass m and are moving with same velocity u, then force on surface is: 

A motorcyclist rides in vertical circle in a hollow sphere of radius 5 m. Find the minimum speed required, so that he does not have any contact with the sphere at the highest point .

A car sometimes overturns while taking a turn. When it overturns, it is

A particle is projected so as to just move along a vertical circle of radius $$r$$ with the help of the massless string. The ratio of the tension in the string when the particle is at the lowest and highest point on the circle is?

A solid sphere is placed on a smooth horizontal plane. A horizontal impluse $$I$$ is applied at a distance $$h$$ above the central line as shown in the figure. Soon after giving the impulse the sphere starts rolling.
The ratio $$h/R$$ would be

A $$1$$m long uniform beam is being balanced as shown in the given figure. What are the forces X and Y?