Force and Mass MCQ Quiz - Objective Question with Answer for Force and Mass - Download Free PDF

Calculation:
The masses M1, M2, and M3 are connected by inextensible strings. Since M1 moves downward with uniform velocity, all three masses move with the same velocity. Thus, the net force on each mass is zero.

Let T1 be the tension in the string connecting M1 and M2, and T2 the tension in the string connecting M2 and M3.

Let the normal reactions be N2 and N3 for masses M2 and M3, and the frictional forces be f2 = μN2 and f3 = μN3.

Apply Newton’s second law on each block:

1. T1 = M1g
2. N2 = M2g cos 37°
3. T1 = T2 + μN2 + M2g sin 37°
4. N3 = M3g
5. T2 = μN3

Now solve the equations:

From (5): T2 = μM3g = 0.25 × 4 × 9.8 = 9.8 N

Substitute into equation (3):

M1g = T2 + μM2g cos 37° + M2g sin 37°

M1 = [T2 + μM2g cos 37° + M2g sin 37°] / g

= [9.8 + (0.25 × 4 × 9.8 × 4/5) + (4 × 9.8 × 3/5)] / 9.8

= [9.8 + 7.84 + 23.52] / 9.8 = 41.16 / 9.8 ≈ 4.2 kg

Answer: M1 = 21/5 kg = 42/10 kg

Solution:

The forces acting on the block are its weight mg, normal reaction N, applied force P, and frictional force f.

Resolve mg along and normal to the inclined plane and apply Newton’s second law:

0 = P + f − mg sinθ

⇒ f = −P + mg sinθ      (1)

This is a straight-line equation with slope −1.

Substitute the values of P1 and P2 in equation (1) to get the frictional force at these points:

f1 = μ mg cosθ,    and    f2 = −μ mg cosθ

So, the graph of frictional force f versus applied force P is a straight line with negative slope, ranging between +μmg cosθ and −μmg cosθ.

Calculation:
3 kg block will be at rest. (So friction between S₂ and D = tension in the string connected to block D)

Considering A + B + C in a system:

T - 6 = 3a
20 - 2T = 2a₁
and a = 2a1   

So, a = 8/7 m/s².

Now, there will be slipping between blocks A and B.

Now, consider (B + C) in a system:

T' - 6 - 1 = 2a'
20 - 2T' = 2a₂

So, T' - 7 = 4a₂
20 - 2T' = 2a₂

So, a' = 1.2 m/s²

Concept:

Three blocks are given and the system of blocks moves with common acceleration.

We have to make individual F.B.D for all the blocks.

Calculation:

Given:​

Acceleration of blocks a = 0.5 m/s².

T₁ is the tension between the mass 4 kg and 6 kg.

T₂ is the tension between mass 10 kg and 6 kg.

T₂ = m₁a

T₂ = 10 × 0.5 = 5 N

T₁ - T₂ = m₂a

T₁ = m₂a + T₂

T1 = (6 × 0.5) + 5 ⇒ 8 N.

∴ the tension between masses 6 kg and 4 kg is 8 N.

CONCEPT:

Forces Acting on a Skydiver

• When a skydiver jumps out of an airplane, they experience two primary forces acting on them: the force of gravity (P) and the force of air resistance or friction (Q).
• The force of gravity (P) pulls the skydiver downward towards the Earth.
• The force of air resistance (Q) acts in the opposite direction, upward, and it increases with the skydiver's speed.

EXPLANATION:

• When the skydiver's parachute is opened, the following happens:
  • Force P (gravity) remains the same because it is dependent on the mass of the skydiver and the gravitational pull, both of which do not change.
  • Force Q (air resistance) increases significantly because the parachute increases the surface area, thereby increasing air resistance.
• Therefore, the correct statement is:

  After the parachute opens, force P remains the same while force Q increases.

Therefore, the correct answer is Option 3: After the parachute opens, force P remains the same while force Q increases.

CONCEPT:

• Force: Force is a push or pulls on an object. A force can cause an object to accelerate, slow down, remain in place, or change shape.

Force exerted = mass x acceleration

⇒ F = m × a

Acceleration = (Final velocity - Initial velocity)/time

⇒ a = (v₂ - v₁) / t

Where F is the force exerted on the body, m is the mass of the body, a is the acceleration of the body, v₂ is the final velocity, v₁ is initial velocity and t s time.

Calculation:

Given data:

the mass of the body m = 4 kg, Final velocity v₂ = 25 m/s, Initial velocity v₁ = 15 m/s, time t = 5 s.

We know that,

⇒ Acceleration = (Final velocity - Initial velocity)/time

a = (25 - 15)/5 m/s² = 2 m/s²

Also,

⇒ Force exerted = mass x acceleration

⇒ Force = 4 × 2 = 8 N

• So option 2 is correct.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or the state of motion is called force.
• Mass is the amount of matter in any substance. It is not a force.
• Weight: The gravitational force acting on any object on the earth's surface is called its weight.
• Tension in a rope: In the ideal case rope is massless and intangible, the force on one side is equal to force on the other side.
• Normal force: It is a force that is exerted by the surface perpendicular to the body. It is a component of the contact force.

EXPLANATION: 

• Since the mass is the amount of matter in a substance which is not a force. Hence option 3 is correct.

CONCEPT:

Force: The interaction that after applying on a body changes or try to change the state of rest or state of motion of the body is called force.

Force (F) = Mass (m) × acceleration (a) 

Retardation: The force acting in the opposite direction to the motion of a body is called the retarding force. This force produces negative acceleration for the body which is called retardation or deacceleration.

Retardation (a) = Force/Mass

The equation of motion is given below:

V = u + a t

Where V is final velocity, u is initial velocity, a is acceleration and t is time

CALCULATION:

Given that: 

Mass of scooter(m) = 120 kg, Initial velocity (u) = 108 km/h

u = (108 × 1000)/3600 m/s = 30 m/s

Force (F) =?

Time taken to stop (t) = 10 sec

Final velocity (V) = 0 m/s​

We know that body is stopped, it means the final velocity is 0. 

V = u + a t

0 = 30 + a × 10

a = -30/10 = - 3 m/s²

Force (F) = m a = 120 × 3 = 360 N

So option 4 is correct.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of the body is called force.

Force (F) = Mass (m) × acceleration (a) 

CALCULATION:

Given that:

Mass of the body (m) = 20 g = 20/1000 = 0.02 kg

Acceleration (a) = 5 cm/s2 = 5/100 = 0.05 m/s²

Force (F) = Mass (m) × acceleration (a) = 0.02 × 0.05 = 1.0 × 10^-3 N

So option 3 is correct. 

CONCEPT:

• Thrust: The force acting perpendicular to the surface of the object is called thrust.
  • When any object is put into the water then the object will replace the water the same as it’s volume and the cause of which there is a force acting upwards, to balance this weight is called the thrust force.
  • Thrust is a kind of pull force, which is applied by the medium on the object.
  • It is a type of force so the SI unit of thrust is Newton (N).
  • The effect of thrust is more on the smaller surface area than the thrust acting on a larger surface area. 

Thrust Force (F_T) = Pressure (P) × Area (A)

EXPLANATION:

• The SI unit of thrust is Newton. So option 4 is correct.
• The SI unit of pressure is the pascal.
• The SI unit of momentum is kg-m/s.
• The SI unit of surface tension is N/m.

​EXTRA POINTS:

• Inertia- It is a kind of resistive force of any object to change its state.
• Momentum- When any massive object moving with a certain velocity, then the momentum of that object will be multiplication of the mass and velocity. The SI unit is kg-m/s
• Volume-It is the quantity of three-dimensional space enclosed by a closed surface.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of the body is called force.

Force (F) = Mass (m) × acceleration (a) 

• Retardation: The force acting in the opposite direction to the motion of a body is called the retarding force. This force produces negative acceleration for the body which is called retardation or deacceleration.

Retardation (a) = Force/Mass

The equation of motion is given below:

V = u + a t

Where V is final velocity, u is initial velocity, a is acceleration and t is time

CALCULATION:

Given that: 

Mass (m) = 10 kg, Initial velocity (u) = 15 m/s

Force (F) = - 50 N

Acceleration (a) = F/m = - 50/10 = - 5 m/s²

Final velocity (V) = 0 m/s

V = u + a t

0 = 15 - 5 × t

So t = 15/5 = 3 sec​

The correct option is Impulse.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or the state of motion is called force.
• Thrust: The force acting perpendicular to the surface of the object is called thrust.
• Impulse (J): The change in momentum is called impulse.
  • It is not a force. It is simply the difference between the two momentum.
• Weight: The gravitational force acting on any object on the earth's surface is called its weight.
• Tension in a rope: In the ideal case rope is massless and intangible, the force on one side is equal to force on the other side.

EXPLANATION: 

• Since the impulse is the change in momentum and it is not a force. Hence option 2 is correct.

The correct answer is Second law of motion.

Key Points

• Newton’s Second Law:
• The rate of change in linear momentum of a body is directly proportional to the external force applied to the body and this change takes place always in the direction of the applied force.
• If a body of mass m moves with velocity \(\vec v\) then its linear momentum can be given by \(\vec p = mv\) and if force \(\vec F\) is applied to a body, then
• \(\therefore \vec F = m a\)
• Where F = Force, m = mass  and a = acceleration
• From the above concept, it is clear that Newton's Second law of motion provides the definition of force.
• The correct option is 1.

Additional Information

• Newton’s First law:
  • A body continues to be in its state of rest or of uniform motion along a straight line unless it is acted upon by some external force to change the state.
  • If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate.
  • Newton’s first law defines inertia and is rightly called the law of inertia.
• Newton’s Third Law:
  • To every action, there is always an equal (in magnitude) and opposite (in direction) reaction.
  • When a body exerts a force on any other body, the second body also exerts an equal and opposite force on the first.
  • Forces in nature always occur in pairs. A single isolated force is not possible.
• The universal law of gravitation:
  • The universal law of gravitation was propounded by Sir Isaac Newton.
  • Newton used the universal law of gravity to prove that the moon is accelerating towards Earth just as a body on Earth is falling towards Earth.
  • According to the Universal law of gravitation, the force between two bodies is directly proportional to their masses and inversely proportional to a square of the distance.
  • The law was given in the year 1687.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of the body is called force.

Force (F) = Mass (m) × acceleration (a) 

CALCULATION:

Given that:

Mass (m) = 100 gm = 100/1000 = 0.1 kg

Acceleration (a) = 10 m/s2

Force (F) = Mass (m) × acceleration (a) = 0.1 × 10 = 1 N

So option 3 is correct.

The correct answer is 150 N.

Key Points

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of the body is called force.

Force (F) = Mass (m) × acceleration (a) 

There are three equations of motion:

V = u + at

V2 = u2 + 2 a S

\({\text{S}} = {\text{ut}} + \frac{1}{2}{\text{a}}{{\text{t}}^2}\)

Where, V = final velocity, u = initial velocity, s = distance traveled by the body under motion, a = acceleration of body under motion, and t = time taken by the body under motion.

CALCULATION:

Given that:

mass of the object (m) = 150 kg.

Time taken (t) = 10 sec.

⇒ Initial velocity = 10 m/s.

⇒ Final velocity = 20 m/s.

Use V = u + at

20 = 10 + a × 10

So a = 1 m/s²

Force = m a  = 150 × 1 = 150 N