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# Law Of Conservation Of Energy - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Law of Conservation of Energy is considered one the most difficult concept.

• 30 Questions around this concept.

## Solve by difficulty

A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work (in Joule) done by the force of gravity during the time the particle goes up is :

A mass of M kg is suspended by a weightless string . The horizontal force that is required to displace it until the string making an angle of 45 with the initial vertical direction is

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement  x is proportional to :

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that :

Consider a rubber ball freely falling from a height onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as function of time will be

The block of  mass M  moving on  the frictionless horizontal  surface collides with the spring of spring constant  and compresses it by length L.The maximum  momentum of the block after collision is

A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m . It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is

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Two hydrogen atoms are in excited state with electrons residing in n = 2. First one is moving towards left and emits a photon of energy $E_1$ towards right. Second one is moving towards right with same speed and emits a photon of energy $E_2$ towards right. Taking recoil of nucleus into account during emission process

The potential energy of a 1 kg particle free to move along the x-axis is given by

$V(x)= \left ( \frac{x^{4}}{4} -\frac{x^{2}}{2}\right )J.$

The total mechanical energy of the particle 2 J. Then, the maximum speed (in m/s) is :

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Which of the following statements best describes the law of conservation of energy?

## Concepts Covered - 1

Law of Conservation of Energy
1. Conservation of Mechanical Energy-

Mechanical energy is the sum of potential energy and kinetic energy.

According to Conservation of Mechanical Energy, If only conservative forces act on a system,

the total mechanical energy remains constant.

By work-energy theorem we have  $W= k_{f}-k_{i}$ or $\bigtriangleup K = \int_{r_{i}}^{r_{f}}\vec{f}.d\vec{s}$ ....(1)

And the change in potential energy in a conservative field is  $\small U_{i}-U_{f}= \int_{r_{i}}^{r_{f}}\vec{f}\cdot \vec{ds}$

Or,   $\small -\bigtriangleup U= \int_{r_{i}}^{r_{f}}\vec{f}\cdot \vec{ds}$  ……..(2)

From equation (1) and (2)

We get, $\small \Delta K=-\Delta U$

$\small \Delta K+\Delta U=0$

Means, $\small K+U=E\left ( constant \right )$

Or, E is constant in a conservative field

i.e; if the kinetic energy of the body increases its potential energy will decrease by an equal amount and vice versa.

1. Law of conservation of total energy-

If some non-conservative force like friction is also acting on the particle, the mechanical energy is no more constant.

It changes by the amount of work done by non-conservative force.

i.e; $\small \Delta K+\Delta U=\bigtriangleup E=W_{fnc}$

The lost energy is transformed into heat or in other forms of energy. But the total energy remains constant.

So, according to the Law of conservation of total energy “Energy may be transformed from one kind to another but it cannot be created or destroyed. The total energy in an isolated system is constant.”

## Study it with Videos

Law of Conservation of Energy

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