Laws of Motion ...

just before the sphere comes in contact with the peg.

if AB is a massless rod,

A particle is given an initial speed $$u$$ inside a smooth spherical shell of radius $$R$$ so that it is just able to complete the circle. Acceleration of the particle, when its velocity is vertical, is

A simple pendulum is released from rest with the string in horizontal position. The vertical component of the velocity of the bob becomes maximum, when the string makes an angle $$\displaystyle \theta $$ with the vertical. The angle $$\displaystyle \theta $$ is equal to

A particle is moving in a circular path in the vertical plane. It is attached at one end of a string of length $$l$$ whose other end is fixed. The velocity at lowest point is $$u$$. The tension in the string is $$\displaystyle \vec{T}$$ and acceleration of the particle is $$\displaystyle \vec{a}$$ at any position. Then $$\displaystyle \vec{T}.\vec{a}$$ is zero at highest point if

What is the maximum speed at which a railway carriage can move without toppling over along a curve of radius $$R=200m$$ if the distance from the centre of gravity of the carriage to the level of the rails is $$h=1.0m$$, the distance between the rails is $$h=1.0m$$, the distance between the rails is $$l=2.0m$$ and the rails are laid horizontally? (Take $$\displaystyle g= 10m/s^{2}$$)

The sphere at A is given a downward velocity $$\displaystyle v_{0}$$ of magnitude $$5 m/s$$ and swings in a vertical plane at the end of a rope of length $$l=2 m$$ attached to a support at $$O$$. Determine the angle $$\displaystyle \theta $$ at which the rope will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere.

A weightless thread can withstand 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 $$g=10\ m/s^2$$, then the maximum angular velocity of the stone will be

A car is travelling along a circular curve that has a radius of 50 m. If its speed is 16 m/s and is increasing uniformly at $$\displaystyle 8 m/s^{2},$$ determine the magnitude of its acceleration at this instant.

A circular tube of mass M is placed vertically on a horizontal surface as shown in the figure. Two small spheres, each of mass m, just fit in the tube, are released from the top. If $$\displaystyle \theta $$ gives the angle between radius vector of either ball with the vertical, obtain the value of the ratio M/m if the tube breaks its contact with ground when $$\displaystyle \theta = 60^{\circ}.$$ Neglect any friction.