A pendulum made of a uniform wire of cross-sectional area A has time period T. When an additional mass M is added to its Bob, the time period changes TM. If Young's modulus of the material of the wire is Y, then 1/Y is equal to (g = gravitational acceleration)

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is (For steel Young’s modulus is 2×10¹¹ N m^–2 and coefficient of thermal expansion is 1.1×10^–5 K^–1 )

• 2.2 x 10⁸ Pa

• 2.2 x 10⁹ Pa

• 2.2 x 10⁷ Pa

• 2.2 x 10⁷ Pa

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10³ kg/m³ and 2.2 × 10¹¹N/m² respectively?

• 188.5 Hz

• 178.2 Hz

• 200.5 Hz

• 200.5 Hz

A wooden wheel of radius R is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that it temperature rises by ∆T and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Youngs'modulus is Y, the force that one part of the wheel applies on the other part is :

• 2πSYα∆T

• SYα∆T

• πSYα ∆T

• πSYα ∆T

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30º with each other. When suspended in a liquid of density 0.8 g cm^–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm^–3, the dielectric constant of the liquid is

• 4

• 3

• 2

• 2

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of

• 81

• 1/81

• 9

• 9

One kg of a diatomic gas is at a pressure of 8 × 10⁴ N/m² . The density of the gas is 4 kg/m^-3. What is the energy of the gas due to its thermal motion?

• 3 × 10⁴ J

• 5× 10⁴ J

• 6× 10⁴ J

• 6× 10⁴ J

8.

Two wires are made of the same material and have the same volume. However wire 1 has cross-section area A and wire 2 has cross–sectional area 3A. If the length of wire 1 increases by ∆x on applying force F, how much force is needed to stretch wire 2 by the same amount?

• F

• 4F

• 9F

• 9F

A transparent solid cylindrical rod has a refractive index of 2√3. It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure.θ The incident angle θ for which the light ray grazes along the wall of the rod is 

If S is stress and Y is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is

• 2S²Y

• S²/2Y

• 2Y/S²

• 2Y/S²