Conservation of Mechanical Energy

A small sphere is attached to a cord and rotates in a vertical circle about a point $O$. If the range speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at:

A stone tied to a string is rotated in a vertical circle. The minimum speed of the stone during a complete vertical circular motion 

A smooth semicircular wire track of radius $R$ is fixed in a vertical plane One end of a massless spring of natural length  $\frac{\mathrm{}\mathrm{}\mathrm{}3R}{4}$  is attached to the lowest point $O$of the wire track. A small ring of mass $m$ which can slide on the track is attached to the other end of the spring. The ring is held stationary at point $P$ such that the spring makes an angle of  $60°$ with the vertical. The spring constant $K=\frac{mg}{R}$ . Consider the instant when the ring is released. Find the normal reaction on the ring by the track.

A small block is shot into each of the four smooth tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

A high speeding bullet of mass $50 \mathrm{g}$ and velocity $100 \mathrm{m} {\mathrm{s}}^{-1}$ passes through a pendulum of mass $1 \mathrm{kg}$ . If the velocity of the bullet gets reduced by $50\%$ after passing through the pendulum, calculate the maximum vertical height till which the pendulum swings.

For a particle in SHM, the K.E. at any instant is given by$K=K_0{\cos }^2\omega t$ .The total energy of SHM is 

A block of mass $2 \mathrm{kg}$is released at point A on a rough platform ($\mu = 0.1$) of mass $10 \mathrm{kg}$ as shown in figure. Block reached point B with velocity $12 \mathrm{m} {\mathrm{s}}^{-1}$ w.r.t. platform find work done by friction?

 An object is projected with a velocity $\sqrt{\frac{8gR}{3}}$ from earth. The velocity of the object, at the maximum height reached by it will be 

A block of mass $m=2 kg$ is pulled by a force$F=40 N$ upwards through a height $h=2 m$. Find the work done on the block by the applied force $F$ and its weight $mg$. (Take, $g=10 m s^{-2}$) 

A block of mass $20 \mathrm{kg}$ is pushed at constant speed from bottom to the top of a frictionless inclined plane of slant length $5 \mathrm{m}$ and height $3 \mathrm{m}$. Then the work done on the block by external force is

A body of mass $20 \mathrm{kg}$ is placed at height of $20 \mathrm{m}$. Then if is allowed to slide and there its speed was $3 \mathrm{m}/\mathrm{s}$ then it comes to a place where its speed becomes 4 m/s. Find the height where it gains a speed of $4 \mathrm{m}/\mathrm{s}$.

The bob of a pendulum of length $L$ is released from the position when the string makes angle $\theta$ with vertical. Find the speed of the bob at the lowest position if no energy is lost due to air friction.

Find the height at which the string becomes stack for the following diagram.

If a ball is allowed to fall freely under the influence of gravity, its

A simple pendulum of length l has a bob of mass 'm'. If it is released from horizontal position, then velocity of the bob at lowest position will be 

A small stone of mass $50 \mathrm{g}$ is rotated in a vertical circle of radius $40 \mathrm{cm}.$ What is the minimum tension in the string at the lowest point? $(\mathrm{g}=10 {\mathrm{ms}}^{-2})$ 

A body is released from position $A$ as shown in figure. The speed of body at position $B$ is

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A heavy particle is suspended by a string of length $l$ from a fixed point $O$. The particle is given a horizontal velocity $v_0$. The string slacks at some angle and the particle proceeds on a projectile path. Find the value of $v_0$, if the particle passes through the point of suspension.

If velocity $v=\sqrt{3gR}$ is given at the mean position, then find the angle where bob will leave circular path?