The spring extends by x on loading, then energy stored by the spring is : (if T is the tension in spring and k is spring constant)

(1) $\frac{{T}^{2}}{2k}$

(2) $\frac{{T}^{2}}{2{k}^{2}}$

(3) $\frac{2k}{{T}^{2}}$

(4) $\frac{2{T}^{2}}{k}$

Concept Questions :-

Elastic potential energy
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Difficulty Level:

The potential energy of a body is given by, U = ABx2 (Where x is the displacement). The magnitude of force acting on the particle is

(1) Constant

(2) Proportional to x

(3) Proportional to x2

(4) Inversely proportional to x

Concept Questions :-

Potential energy: Relation with force
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Difficulty Level:

The potential energy between two atoms in a molecule is given by $U\left(x\right)=\frac{a}{{x}^{12}}-\frac{b}{{x}^{6}}$; where a and b are positive constants and x is the distance between the atoms. The atoms are in stable equilibrium when:

(1) $x=\sqrt[6]{\frac{11a}{5b}}$

(2) $x=\sqrt[6]{\frac{a}{2b}}$

(3) x = 0

(4) $x=\sqrt[6]{\frac{2a}{b}}$

Concept Questions :-

Potential energy: Relation with force
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Difficulty Level:

Which one of the following is not a conservative force

(1) Gravitational force

(2) Electrostatic force between two charges

(3) Magnetic force between two magnetic dipoles

(4) Frictional force

Concept Questions :-

Work-Energy theorem
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Difficulty Level:

Work done in raising a box depends on

(1) How fast it is raised

(2) The strength of the man

(3) The height by which it is raised

(4) None of the above

Concept Questions :-

Gravitational Potential energy
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Difficulty Level:

A frictionless track ABCDE ends in a circular loop of radius R. A body slides down the track from point A which is at a height h = 5 cm. Maximum value of R for the body to successfully complete the loop is

(1) 5 cm

(2) $\frac{15}{4}\text{\hspace{0.17em}}cm$

(3) $\frac{10}{3}\text{\hspace{0.17em}}cm$

(4) 2 cm

Concept Questions :-

Work-Energy theorem
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Difficulty Level:

If the water falls from a dam into a turbine wheel 19.6 m below, then the velocity of water at the turbine is (g = 9.8 m/s2)

(1) 9.8 m/s

(2) 19.6 m/s

(3) 39.2 m/s

(4) 98.0 m/s

Concept Questions :-

Gravitational Potential energy
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Difficulty Level:

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density; $\rho$. The height of the liquid in one vessel is h1 and that in the other vessel is h2 $\left({h}_{1}>{h}_{2}\right)$.The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected is :

(1) $\left({h}_{1}-{h}_{2}\right)g\rho$

(2) $\left({h}_{1}-{h}_{2}\right)gA\rho$

(3) $\frac{1}{2}{\left({h}_{1}-{h}_{2}\right)}^{2}gA\rho$

(4) $\frac{1}{4}{\left({h}_{1}-{h}_{2}\right)}^{2}gA\rho$

Concept Questions :-

Gravitational Potential energy
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Difficulty Level:

If the increase in the kinetic energy of a body is 22%, then the increase in the momentum will be

(1) 22%

(2) 44%

(3) 10%

(4) 300%

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Difficulty Level:

If a body of mass 200 g falls from a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface, then what is the decrease in P.E. of the body at the contact (g = 10 m/s2)

(1) 200 J

(2) 400 J

(3) 600 J

(4) 900 J