Potential Energy

A conservative force of ($-3\hat{i}$) $\mathrm{N}$ acts on a body of mass $3 \mathrm{kg}$. The change in potential energy of the body due to the force, when it undergoes a displacement $\left(6\hat{i}\right)m$ is

 

The variation of potential $U$ of a body moving along $X$ axis varies with the position $x$ as shown in the figure.The body is in equilibrium state in

For the situation shown in the figure, horizontal spring and the spring connecting blocks $B$ and $C$ are light. The blocks $A,B$ and $C$ are of same mass $m$. The pulley is smooth and fixed. The accelerations of $A, B$ and $C$ just after cutting the horizontal spring are

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The force exerted by a special compression device is given as function of compression $x$ as $F_x\left(x\right)=kx\left(x-l\right)$ for $0\le x\le l$, where $l$ is the maximum possible compression and $k$ is a constant. The force exerted by the device under compression is maximum when compression is:

In the given diagram system is in equilibrium. If applied force $F$ is doubled how much distance, the mass less block will more towards right before new equilibrium is achieved.

As shown in the figure, an iron block $A$ of volume $0.25 {\mathrm{m}}^3$ is attached to a spring $S$ of unstretched length $1.0 \mathrm{m}$ and hanging to the ceiling of a roof. The spring gets stretched by $0.2 \mathrm{m}$. This block is removed and another block $B$ of iron of volume $0.75 {\mathrm{m}}^3$ is now attached to the same spring and kept on a frictionless incline plane of $30°$ inclination. The distance of the block from the top along the incline at equilibrium is

Two blocks $A$ and $B$ of equal mass $2\mathrm{kg}$ are arranged as shown with springs $S_1$ and $S_2$. Spring $S_2$ is pulled with force $F=6 \mathrm{N}$. Acceleration of block $B$ is $4 \mathrm{m} {\mathrm{s}}^{-2}$ towards right at an instant. If $F$ is suddenly removed at this instant, the instantaneous acceleration of $A$ and $B$ will be (assume no friction)

A bead of mass $m$ moves along a smooth fixed ring in a gravity free region. The ring has radius $R$. The bead is attached to a spring of force constant $K$ and natural length $R$. The other end of the spring is fixed to a point $P$ on the ring. At an instant shown in the figure when length of spring was $1.6 R$, force applied by the ring on the bead was zero. Rate of change of speed of the bead at this instant will be

A particle of mass $2\mathrm{kg}$ is attached with a spring of stiffness $72 \mathrm{N} {\mathrm{m}}^{-1}$. When block is at $x=1 \mathrm{m}$ it moves with maximum speed. The block moves with $24 \mathrm{m} {\mathrm{s}}^{-1}$ while passing through $x=4 \mathrm{m}$. Find out the $x$ coordinates in $\mathrm{m}$ where it's velocity will be zero.

A spring $40 \mathrm{mm}$ long is stretched by the application of a force. If $10 \mathrm{N}$ force required to stretch the spring through $1 \mathrm{mm}$, then work done in stretching the spring through $40 \mathrm{mm}$ is

When, two ends of an ideal spring are pulled apart increasing its length it produces force equal to $kx$ at its ends. At a point $\frac{1}{4}$ of its length from one end, the force is

Two blocks $A\&B$ with mass $4 \mathrm{kg}$ and $6 \mathrm{kg}$ respectively are connected by a stretched spring of negligible mass as in figure. When the two blocks are released simultaneously the initial acceleration of $B$ is $1.5 \mathrm{m}/{\mathrm{s}}^2$ westward. The acceleration of $A$ is:

The spring constant of the spring of a gun is $k$ newton/meter. The spring has been compressed $x$ meter from its normal position and a bullet of mass $m$ has been put in the barrel. If the friction is negligible then on firing the gun, the bullet shall have a velocity of $\left(\mathrm{m}/\sec \right):$

From a fixed support $\mathrm{O}$, hangs an elastic string of negligible mass and natural length $L$. Masses $m_1$ and $m_2$ attached at the lower end, elongate the string to $2 \mathrm{L}$. When $m_2$ is removed gently, $m_1$ is able to bounce back to $\mathrm{O}$. The ratio $m_2/m_1$ is (assume that the string does not obstruct the motion of $m_1$ )

The system shown in the figure is released from rest. Pulley and spring are massless and friction is absent everywhere. The speed of $5 \mathrm{kg}$ block when $2 \mathrm{kg}$ block leaves the contact with ground is $\left(K=40 \mathrm{N} {\mathrm{m}}^{-1} \& \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

$K$ is the force constant of a spring. The work done in increasing its extension from $l_1$ to $l_2$ will be

Water stored in a dam posseses

A body is falling from a height h. After it has fallen a height h/2, it will possess_____.

Water stored in a dam possesses_____.

A car is accelerated on a levelled road and attains a velocity 4 times of its initial velocity. In this process the potential energy of the car_____.