Laws of Motion ...

A simple pendulum is oscillating with an angular amplitude $$60^o$$. If $$m$$ is mass of bob and $$T_1$$, $$T_2$$ are tensions in the string, when the bob is at extreme position, mean position respectively then is:

The length of a simple pendulum is  '$$L$$'. Its bob from rest position is projected horizontally with a velocity $$\sqrt{\dfrac{7gL}{2}}$$. The maximum angular displacement of bob, such that the string does not slack, is:

The length of a ballistic pendulum is $$1 m$$ and mass of its block is $$1.9 kg$$. A bullet of mass $$0.1 kg$$ strikes the block of ballistic pendulum in horizontal direction with a velocity $$100ms^{–1}$$ and got embedded in the block. After collision the combined mass (block & bullet) swings away from lowest point. The tension in the string when it makes an angle $$60°$$ with vertical is  $$(g=10ms^{-2})$$:

A simple pendulum is oscillating with an angular amplitude $$60^{0}$$. If mass of bob is $$50\ gram$$, the tension in the string at mean position is:
$$(g=10\ m/s^{2})$$

The bob of a simple pendulum of mass $$'m'$$ is performing oscillations such that the tension in the string is equal to twice the weight of the bob while it is crossing the mean position. The tension in the string when the bob reaches extreme position is :

Mass of the bob of a simple pendulum of length $$L$$ is $$m$$. If the bob is projected horizontally from its mean position with velocity $$\sqrt{4gL}$$ , then the tension in the string becomes zero after a vertical displacement of :

Two bodies A, B of masses $$m_1, m_2$$ are knotted to a mass-less string at different points rotated along concentric circles in horizontal plane. The distances of A, B from common centre are 50cm, 1m. If the tensions in the string between centre to A and A to B are in the ratio 5:4, then the ratio of $$m_{1}$$ to $$m_{2}$$ is:

A simple pendulum consists of a light string from which a spherical bob of mass, $$M$$, is suspended. The distance between the point of suspension and the center of bob is $$L$$. At the lowest position, the bob is given tangential velocity of $$\sqrt{5gL}$$. The K.E of the bob when the string becomes horizontal is:

A curved road is $$7.5\ m$$ wide and its outer edge is raised by $$1.5\ m$$ over the inner edge. The radius of curvature is $$50\ m$$. For what speed of the car is this road suited?$$(g=10m/s^{2})$$:

The bob of a simple pendulum is given a velocity in horizontal direction when the bob is at lowest position ,so that the bob describes vertical circle of radius equal to length of pendulum and tension in the string is $$10 \ N$$ when the bob is at an angle $$60^0$$ from lowest position of vertical circle. The tension in the string when the bob reaches highest position is (The mass of bob is $$ 100$$ gram. $$g = 10\ ms^{–2}$$):