Download all Maths Solution: Sample Questions on Work, Energy And Power

Sample Questions On Work, Energy And Power

Q:1- An engine of 2 × 10⁶ kW power is drawing a train of total mass of 3.0 × 10⁶ kg up an inclined plane, inclined at an angle of 60°. The frictional force is 8 × 10³ N. What is the maximum speed of the train?(Ans: 78.7 m/s.)

Q:2- A bullet of mass 15 grams moving with a velocity of 350 m/s enters a block of length 1.2 metres and goes out of the other side with a velocity of 290 m/s. What is the work done by the bullet in passing through the block?(Ans: 288 J.)

Q:3- A block of mass of 500 grams starts from the top of a frictionless curved hill top with an initial speed of 2 m/s, it arrives at the bottom of the hill with a speed of 3.5 m/s.What is the height of the hill?(Ans:0.42 m. )

Q:4- An iron ball of 0.2 kg, which is moving with a speed of 12 m/s, collides with an identical steel ball at rest. After collision the direction of each ball makes an angle of 45° with the original direction. What is the speed of the iron balls after the collision?(Ans: 8.48 m/s.)

Q:5- A motor of 2 kW power is able to pump out water from a well 12 m deep. What quantity of water is being pumped out per second?(Ans: 17.01 kg.)

Q:6- The bob of a pendulum is able to rise to vertical height of 15 cm. What is the velocity of the bob at its mean position?(Ans: 1.71 m/s.)

Q:7- A drop of water of radius 1.5 mm falls from a height of 60 cm. What is the work done by the gravitational force on the drop?(Ans: 8.3 × 10⁻⁵ J.)

Q:8- A body of mass 3.2 kg, which was at rest initially, is subjected to a force of 12 N for 10 seconds. What is the kinetic energy acquired by the body?(Ans: 2250 J.)

Q:9- A bullet of mass 30 grams passes between the two ends of a 40 metres long road in 0.3 seconds. The bullet travels with a constant speed. What is the kinetic energy of the bullet?(Ans: 266.66 J.)

Q:10-Work done by the boy in the given figure is 250 J per second. The speed of the boy is 1.2 m/s.

What is the force applied by the boy?(Ans: 294.6 N.)

Q:11- The linear momentum of a body is increased by 21%. What is the percentage increase in kinetic energy?(Ans: 46.41 %.)

Q:12-A motor is used to pump water from a well, and rise to a height of 12 m. The power of the motor 3 kW. The amount of water raised per minute by the motor is (Ans: 1530.61 kg.)

Q:13- A body of mass 2 kg falls from a height of 8 m and collides with another body of the same mass. After collision, the two bodies move through a distance of 2 m and ultimately come to rest. What is the work done against the resistive force?(Ans: 156.8 J.)

Q:14- A ball of mass 350 grams is dropped from a height of 12 metres; it rebounds from the hard floor. It loses 30 % of the energy in impact. The height to which the ball would rise after the impact is (Ans: 3.6 m.)

Q:15- Momentum for a body is twice the magnitude of kinetic energy of the body. What is the velocity of the body?(Ans: 1 unit. )

SOLUTIONS

Answer:1-

Power of the engine,

P = 2 × 10⁶ kW = 2 × 10⁶ kW
Mass of the train, m = 3 × 10⁶ kg
Frictional force = 8 × 10³ N
Angle of the inclined plane,
θ = 60°
Acceleration due to gravity, g = 9.8 m/s²
Force, F = mg sin θ + f

Therefore, the velocity of the train is 78.7 m/s.

Answer:2-

Mass of the bullet, m = 15 g = 0.015 kg
Initial velocity, v₀ = 350 m/s
Final velocity, v = 290 m/s
Work done by the bullet = loss in kinetic energy

Therefore, the work done by the bullet is 288 J.

Answer:3-

Mass of the block, m = 500 g = 0.5 kg
Initial speed of the block, u = 2 m/s
Final speed of the block v = 3.5 m/s
Acceleration due to gravity, g = 9.8 m/s²
Let h be the height of the hill.
The track is frictionless, so the mechanical energy will be conserved
Energy at the top of the hill

Energy at the base of the hill

Equating (1) and (2),

Hence, the height of the toy hill is 0.42 m.

Answer:4-

Mass of the iron ball, m₁ = 0.2 kg
Initial velocity of iron ball, v₁ = 12 m/s
Mass of the other iron ball, m₂ = 0.2 kg
The second ball is at rest.
Initial velocity of the second ball, v₂ = 0
Along x-axis,
Applying the law of conservation of momentum,

Where,

is the final velocity of the first ball.

is the final velocity of the second ball.

is the angle of deflection of the ball = 45°

Along y-axis,
Applying law of conservation of momentum,

From equation (1) and (2),

The final velocity of both the balls is 8.48 m/s.

Answer:5-

Power of the motor, P = 2 kW = 2 × 10³ W
Depth of the well, h = 12 m
Acceleration due to gravity = g = 9.8 m/s²
Energy = mgh
Where m is the mass of water.
Time, t = 1s
Power ,

Therefore, the mass of water pumped out per second is 17.01 kg.

Answer:6-

According to the principle of conservation of energy, the kinetic energy the bob at the mean position is equal to the potential energy at the maximum vertical height.
Kinetic energy of the bob at mean position =

Potential energy of the bob at maximum vertical height = mgh
Where,
m is the mass of the bob.
v is the velocity of the bob at the mean position.
g is the acceleration due to gravity = 9.8 m/s²
h is the height reached by the bob = 15 cm = 0.15

Therefore, the velocity of the bob in the mean position is 1.71 m/s.

Answer:7-

Radius of the water drop, r = 1.5 mm = 1.5 × 10⁻³ m
Height of the drop from the ground, h = 60 cm = 0.6 m
Volume of the drop,

Density of water, ρ = 1000 kg/m³
Mass of water, m = Vρ

Acceleration work done by the gravitational force = mgh

Therefore, the work done by the gravitational force on the drop of water is 8.3 × 10⁻⁵ J.

Answer:8-

Mass of the body, m = 3.2 kg
Force applied, F = 12 N
Time for which force is applied, t = 10 s.
The body is at rest initially.
∴Initial velocity, u = 0
Let, a be the acceleration of the body, and v be the final velocity of the body.

Kinetic energy =

Therefore, kinetic energy possessed by the body is 2250 J.

Answer:9-

Mass of a bullet, m = 30 g = 0.0 3 kg
Distance covered by the bullet, d = 40 cm
Time taken to cover the distance, t = 0.3s.
Speed,

Kinetic energy,

Therefore, the kinetic energy of the bullet is 266.66 J.

Answer:10-

Work done by the man, W = 250 J
Speed of the man, v = 1.2 m/s
Angle made by the direction of force to the horizontal θ = 45°
Let F be the force applied by the boy.

S is the distance traveled in 1s = 1.2 m/s × 1s
∴S = 1.2 m

Therefore, the force applied by the boy is 294.6 N.

Answer:11-

Let m be the mass of the body.
v₁, be the initial velocity of the body.
v₂ be the final velocity of the body.
The linear momentum increased by 21%.

Initial kinetic energy,

Final kinetic energy,

Percentage increase in kinetic energy

Therefore, the percentage increase in kinetic energy is 46.41 %.

Answer:12-

ower of the motor, P = 3 kW = 3 × 10³ W
Height to which the water is raised, h = 12 m
Acceleration due to gravity, g = 9.8 m/s².
Time for which the water is been lifted, t = 1 min = 60 s
Let m be the mass water been raised.

Therefore, the amount of water raised per minute is 1530.61 kg.

Answer:13-

Mass of both the body, m = 2 kg
Height from which the body falls, h = 8m
Distance covered by both the bodies together, d = 2 m
Acceleration due to gravity, g = 9.8 m/s²
According to the principle of conservation of energy,
mgh

Where, v is the velocity of the first body.

Let v′ be velocity of both bodies together.

Work done against the resistive force

Therefore, the work done against the resistive is 156.8 J.

Answer:14-

Mass of the ball, m = 350 g = 0.35 kg.
Height from which the ball is dropped, h = 12 m
Acceleration due to gravity, g = 9.8 m/s².
Energy loss after impact = 30 %
Let h₁ be the height to which the ball would rise after the impact.