Laws of Motion ...

A circular track of radius $$100$$ m is designed for an average speed $$54$$ km/h. Find the angle of banking.

A force of 10 N acts on a body for 3 microsecond $$(\mu s)$$. Calculate the impulse. If mass of the body is 5 g, calculate the change of velocity.

Which of the following must be true for the sum of the magnitude of the momenta of the individual particles in the system?

Water in a bucket is whirled in a vertical circle with a string to it. The water does not fallen even when the bucket is inverted at the top of its path . We conclude that in this position:

 A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $$\overrightarrow{a}$$ is correctly shown in

The magnitude of force (in $$N$$) acting on a body varies with time $$t$$ (in $$\mu s)$$ as shown. $$AB, BC$$ and $$CD$$ are straight line segments. The magnitude of total impulse of force on the body from $$t=4\mu s$$ to $$t=16\mu s$$ is :

A stone tied to string of length $$l$$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time the stone is at its lowest position and has a speed $$u$$. The magnitude of the change in velocity as it reaches a position, where the string is horizontal is

A stone of mass $$1000g$$ tied to a light string of length $$10/3m$$ is whirling in a vertical circle. If the ratio of the maximum tension to minimum tension is $$4$$ and $$g=10{ ms }^{ -2 }$$, then the speed of stone at the highest point of circle is :

A particle of mass, $$m$$, is tied to a light string and rotated with a speed, $$v$$, along a circular path of radius, $$r$$. If $$T=$$ tension in the string and $$mg =$$ gravitational force on the particle, then the actual forces acting on the particle are

A stone of mass $$1\ kg$$ tied to a light inextensible string of length. $$L = \dfrac{10}{3}$$ metre is whirling in a circular path of radius, $$L$$, in a vertical plane. If the ratio of maximum tension to the minimum tension is $$4$$ and if $$g$$ is taken to be $$10\ m/s^{2}$$, the speed of the stone at the highest point of circle is :