Physics - Elasticity and Young's Modulus

Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be

• 1 : 2

• 1 : 4

• 2 : 1

• 1 : 1

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

The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If Y_A and Y_B are the Young 's moduli of the materials, then

• Y _B = 2Y_A

• Y_B = Y_A

• Y_B =3Y_A

• Y_A =3Y_B

The Young's modulus of a wire is Y. If the energy per unit volume is E, then the strain will be

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

In steel, the Young's modulus and the strain at the breaking point are 2 × 10¹¹ Nm^-2 and 0.15 respectively. The stress at the breaking point for steel is therefore

• 1.33 x 10¹¹ Nm^-2

• 1.33 x 10¹² Nm^-2

• 7.5 x 10^-13 Nm^-2

• 3 x 10¹⁰ Nm^-2

A wire of length L and cross-sectional area A is made of material of Young's modulus Y. The work done in stretching the wire by an amount x is

A steel wire of diameter 2 mm has breaking strength of 4 × 10⁵ N. What is the breaking force of similar steel wire of diameter 1.5 mm?

• 2.3 × 10⁵ N

• 2.6 × 10⁵ N

• 3 × 10⁵ N

• 1.5 × 10⁵ N

The breaking stress of aluminium is 7.5 × 10⁷ Nm^-2. The greatest length of aluminium wire that can hang vertically without breaking is (Density of aluminium is 2.7 × 10³ kg m^-3)

• 283 × 10³ m

• 28.3 × 10³ m

• 2.83 × 10³ m

• 0.283 × 10³ m

A brass rod of cross-sectional area 1 cm² and length 0.2 m is compressed lengthwise by a weight of 5 kg. If Young's modulus of elasticity of brass is 1 × 10¹¹ N/m² and g = 10m/ sec², then increase in the energy of the rod will be

• 10^-5J

• 2.5 × 10^-5J

• 5 × 10^-5J

• 2.5 × 10^-4J