During elastic impact, the relative velocity of the two bodies after impact is __________ the relative velocity of the two bodies before impact.

Ball ‘A’ of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/s hits an identical stationary ball ‘B’ on the table. If the impact is perfectly elastic, the velocity of the ball ‘B’ just after impact would be

A

Zero

B

5 m/sec

C

10 m/sec

D

None of these

A ball moving with a velocity of 5 m/sec impinges a fixed plane at an angle of 45° and its direction after impact is equally inclined to the line of impact. If the coefficient of restitution is 0.5, the velocity of the ball after impact will be

A

0.5 m/sec

B

1.5 m/sec

C

2.5 m/sec

D

3.5 m/sec

Newton's law of Collision of elastic bodies states that when two moving bodies collide each other, their velocity of separation

A

Is directly proportional to their velocity of approach

B

Is inversely proportional to their velocity of approach

C

Bears a constant ratio to their velocity of approach

D

Is equal to the sum of their velocities of approach

If u₁ and u₂ are the velocities of two moving bodies in the same direction before impact and v₁ and v₂ are their velocities after impact, then coefficient of restitution is given by

A

$$\frac{{{{\text{v}}_1} - {{\text{v}}_2}}}{{{{\text{u}}_1} - {{\text{u}}_2}}}$$

B

$$\frac{{{{\text{v}}_2} - {{\text{v}}_1}}}{{{{\text{u}}_1} - {{\text{u}}_2}}}$$

C

$$\frac{{{{\text{u}}_1} - {{\text{u}}_2}}}{{{{\text{v}}_1} - {{\text{v}}_2}}}$$

D

$$\frac{{{{\text{u}}_2} + {{\text{u}}_1}}}{{{{\text{v}}_2} + {{\text{v}}_1}}}$$

Three elastic constants for a completely anisotropic elastic material which follows the Hooke's law are young's modulus, elastic limit stress and yield stress. Which of the following properties is most sensitive to increase in strain rate ?

A

Tensile strength

B

Elastic limit

C

Proportional limit

D

Yield strength

Elastic failure of a material occurs, when the tensile stress equals yield strength, yield point or the elastic limit. Also, the elastic failure occurs according to maximum strain theory, when the maximum tensile strain equals (where, σ = yield strength and E = modulus of elasticity)

A

E

B

Σ

C

Σ/E

D

E/σ

Elastic failure of a material occurs, when the tensile stress equals yield strength, yield point or the elastic limit. Also, the elastic failure occurs according to maximum strain theory, when the maximum tensile strain equals (where, $$\sigma $$ = yield strength and E = modulus of elasticity)

A

E

B

$$\sigma $$

C

$$\frac{\sigma }{{\text{E}}}$$

D

$$\frac{{\text{E}}}{\sigma }$$

Two balls of equal mass and of perfectly elastic material are lying on the floor. One of the balls with velocity ‘v’ is made to strike the second ball. Both the balls after impact will move with a velocity

A

$${\text{v}}$$

B

$$\frac{{\text{v}}}{2}$$

C

$$\frac{{\text{v}}}{4}$$

D

$$\frac{{\text{v}}}{8}$$

Which of the following statements are correct? 1) Velocity compounded impulse turbine gives less speed and less efficiency. 2) For an ideal centrifugal compressor, the pressure produced depends on impeller velocity and diameter. 3) While flowing through the rotor blades in a gas turbine, the relative velocity of gas continuously decreases. 4) While flowing through the rotor blades in an axial flow compressor, the relative velocity of air continuously decreases.

A

1 and 3

B

2 and 3

C

1 and 4

D

2 and 4

A ball of mass 1 kg moving with a velocity of 2 m/sec collides a stationary ball of mass 2 kg and comes to rest after impact. The velocity of the second ball after impact will be

A

Zero

B

0.5 m/sec

C

1.0 m/sec

D

2.0 m/sec

During elastic impact, the relative velocity of the two bodies after impact is __________ the relative velocity of the two bodies before impact.

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