Work done MCQ Quiz - Objective Question with Answer for Work done - Download Free PDF

Calculation:
(I) Given: 0 = 100v + 50(v + 3) (COLM) v = -1 m/s So, work done by man is:

W = (1/2)(100)(1)² + (1/2)(50)(2)² = 150 J   

(II) W_W + W_mg = Δ K.E. (WET) W_N = (1/2)(2)(10)² - (1/2)(2)(5)² = -100 J

(III) Unstable equilibrium points are x = 10 m, 30 m. Stable equilibrium point is x = 20 m. So, U_i = 0, and U_f = -(1/100)(10)⁴ = -100 J. Work done by conservative force is: W_{conservative force} = U_i - U_f = 0 - (-100) = 100 J

(IV) W_ext = U_f - U_i = mg( (5R/8) - (3R/8) ) = mgR/4 = 100 J

The correct answer is option 4) i.e. 

CONCEPT:

• Work is said to be done by a force when the force acting on it causes the object to displace.

Mathematically it is given by;

W = F.x = Fxcosθ 

Where F is the force acting on the object and x is the displacement caused.

• The force acting on an object and displacement is represented graphically as shown. 
  • Consider a varying force acting on the object. If we divide the region under the curve into infinitesimally small regions, the force would appear constant for that region which has caused a displacement of Δx. 
  • In such a case, the area of that small region = Force × displacement (Δx) = work done.

Therefore, work done by a variable force is given by:

​

EXPLANATION:

Let x be the distance covered. Given that 

Work done,

Calculation:

Calculation:

W_all = Δk

W_e = k_f – k_i

Calculation:

Work done

= 

The correct answer is Zero.

Key Points

• When an object rotates in a circle the work done is zero because, in a circular motion, the displacement is always perpendicular to the applied force.
• Also, when a body moves along a circle, the centripetal force acts along the radius of the circle and is perpendicular to the motion of the body.

Important Points

• Work done:
  • work done is defined as the multiplication of the magnitude of the displacement d and the component of the force in the direction of the displacement.
  • Work done through force (F) is equal to a change in kinetic energy.

CONCEPT:

• Work done: It is the dot product of Force and Displacement.

where W is the work done, F is the force, d is the displacement, and θ is the angle between F and d.

CALCULATION:

Given that W = 1J; F = 10N; d = 10cm = 0.1m; 

Work done is given by 

1 = cosθ 

cos 0° = cosθ

θ = 0° 

• So the angle between force and displacement is 0°
• Hence the correct answer is option 4.

CONCEPT:​

• Work done: It is the dot product of Force and Displacement.

⇒ Work Done (W) = Force (F) × Displacement (S) × cos θ 

where θ is the angle between force and displacement.​

• The gravitational force or weight of a body always acts in the downward direction.

EXPLANATION:

• When a car is moving in a horizontal path, at any particular time,
  • The direction of gravity force is downwards and
  • The direction displacement will be in the direction of motion that is the horizontal direction (perpendicular to the downward direction).

• So the angle between gravity force and displacement will be θ = 90.

⇒ Work Done (W) = Gravity Force (F) × Displacement (S) × cosθ 

⇒ W = F × S × cos90°

⇒ W = F × S × 0 = 0

• So the correct answer is option 1.

Option 2 is correct, i.e. W = F.S cosθ.

CONCEPT:

• Work: Work is said to be done by a force when the body is displaced actually through some distance in the direction of the applied force.
• Since the body is being displaced in the direction of F, therefore work done by the force in displacing the body through a distance s is given by:

Or, W = Fs cos θ

• Thus work done by a force is equal to the scalar or dot product of the force and the displacement of the body.

EXPLANATION:

Work done (W) = F.s cosθ 

So option 2 is correct.

CONCEPT:

• Work: Work is said to be done by a force on an object if the force applied causes a displacement in the object.
• The work done by the force is equal to the product of force and the displacement in the direction of the force.
• Work is a scalar quantity.
• Its SI unit is Joule(J).

In vector form,

Where W = work done, F = force, x = displacement and θ = angle between F and x

CALCULATION:

Given  and 

The work done by the force is:

Hence, option 3 is correct.

CONCEPT:

• Centripetal Force: The force that makes a body to move in a circular motion is known as centripetal force.
  • The direction of this force is always towards the center.

The centripetal force acting on a body of mass 'm' revolving with radius 'r' is:

• Work done: It is the dot product of Force and Displacement.

Work Done (W) = Force (F) × Displacement (S) × cosθ 

where θ is the angle between force and displacement.​

EXPLANATION:

• When a body is moving in a circular path, at any particular time,
  • The direction centripetal force is towards centre and
  • The direction displacement will be in the direction of motion that is perpendicular to the centripetal direction.

• So the angle between centripetal force and displacement will be θ = 90.

Work Done (W) = Centripetal Force (F) × Displacement (S) × cosθ 

W = F × S × cos90°

W = 0

• So the correct answer is option 3.

CONCEPT:

• Work (W) is said to be done by a force when the force acting on it causes the object to displace.
• Mathematically it is given by:

Where F = The magnitude of the force vector, d = The magnitude of the displacement vector

EXPLANATION:

Given: The pull force F is applied in the antiparallel direction to the displacement of the mass on the plane.

• Referring to the diagram,

• So, the displacement and pulling force vectors will be in the antiparallel direction to each other as the angle between them will be 180°.

∵ θ  = 180°.⇒ cos180° = -1 

• So, using equation 1,
• The work done in pulling the mass M  will be negative as the magnitude of the force and displacement vector can not be negative.

So, the correct answer will be option 4.

Concept:

Elastic potential energy: It is the potential energy created when an object undergoes an elastic deformation due to a force applied to it.

• This energy is stored in the object as long as the force is in action and the object goes back to its original shape when the force is removed.
• A spring undergoes a similar situation when a force acting on it causes a displacement due to elastic deformation.

The potential energy (U) required to stretch a string by x distance is given by

where k is the spring constant.

Calculation:

Given:

Let the potential energies of the spring be U₁ and U₂ when they are stretched be x₁ and x₂ respectively.

Given that: U₁ = U

When x₁ = 2 cm:

    ------ (1)

When x₂ = 10 cm:

    ------- (2)

On dividing equations (1) and (2), we get

⇒ U₂ = 25U₁ = 25U