Laws of Motion MCQ Quiz - Objective Question with Answer for Laws of Motion - Download Free PDF

Calculation:

Inertial Frame of Reference (Ground):

The free body diagram (FBD) of the block with respect to the ground is shown below.

With respect to the ground, the block is moving with an acceleration a. Therefore:

∑Fy = 0 (sum of forces in the vertical direction) and ∑Fx = ma (sum of forces in the horizontal direction)

mg = μN and N = ma

Thus, the acceleration a is:

a = g / μ

Using this in the equation for the horizontal force:

F = (M + m) × a = (M + m) × (g / μ)

Solution:

The distance between the two particles initially is 12 + 3 = 15 m.

Distance covered by particle-1 (S1): u1t + (1/2) a1 t2

Distance covered by particle-2 (S2): u2t + (1/2) a2 t2

Since they move towards each other, the sum of distances covered equals 15 m:

S1 + S2 = 15

Substitute the given values (consider directions):

(-5)t + (1/2)(+3)t2 + (7)t + (1/2)(-2)t2 = 15

⇒ -5t + 1.5t2 + 7t - t2 = 15

⇒ 2t + 0.5t2 = 15

⇒ 4t + t2 = 30

⇒ t = [-4 ± √136] / 2

Only the positive root is valid, so:

t ≈ [-4 + 11.66] / 2 ≈ 7.66 / 2 ≈ 3.83 seconds

Tthe x-coordinate of collision

Displacement of particle-1:

S1 = u1t + (1/2) a1 t2

S1 = (-5)(3.83) + 0.5 × 3 × (3.83)2

S1 ≈ -19.15 + 0.5 × 3 × 14.66 ≈ -19.15 + 21.99 ≈ 2.84 m

So, the x-coordinate of collision:

xcollision = Initial position of particle-1 + S1

xcollision = -12 + 2.84 ≈ -9.16 m

(b) x-coordinate of collision ≈ -9.16 m

Calculation:

For the pulling case: The pulling force F_pull has both a horizontal component F_pull cos(θ) and a vertical component F_pull sin(θ).

Using Newton's second law and balancing forces, we find that the condition for pulling force is:

F_pull = μmg / (cos(θ) + μsin(θ))

For the pushing case: The pushing force F_push also has a horizontal component F_push cos(θ) and a vertical component F_push sin(θ).

The condition for the pushing force is:

F_push = μmg / (cos(θ) - μsin(θ))

For the pulling and pushing forces to be equal, we set F_pull = F_push. This occurs when the angle θ = 0°, which simplifies the equations to:

F_pull = F_push = μmg

Thus, the pulling and pushing forces are equal when the angle of application is 0°, and the value of the forces is mg.

Therefore, the correct answer is (A).

Calculation:

The velocity v of a point on the surface of the expanding sphere with instantaneous radius r is directed radially outward. Its magnitude is given by v = dr/dt.

The density of the sphere, with mass m, is given by ρ = m / (4/3 π r³).

Differentiating with respect to time t, we get:

dr/dt = (1/3) × (3m / (4π r⁴)) × (dρ/dt) = - r / 3ρ × (dρ/dt)

⇒ a = (1 / 3ρ × (dρ/dt))² r

Since m and (1 / ρ × dρ/dt) are constants,

Putting the value, we get k = 1

Thus, the correct answer is option 4.

​Calculation:

Given: Mass m = 1 kg, g = 10 m/s²

Angles: T₁ at 60°, T₂ at 30°

Vertical equilibrium condition:

T₁cos60° + T₂cos30° = mg = 10

Horizontal equilibrium condition:

T₁sin60° = T₂sin30°

Now use sin and cos values:

sin60° = √3/2, sin30° = 1/2

cos60° = 1/2, cos30° = √3/2

From horizontal: T₁(√3/2) = T₂(1/2)

⇒ T₁ = T₂ / √3

Substitute in vertical:

(T₂/√3)(1/2) + T₂(√3/2) = 10

⇒ T₂[1/(2√3) + √3/2] = 10

T₂ = (10 × √3) / 2 = 5√3 N

Now, T₁ = T₂ / √3 = (5√3) / √3 = 5 N

Hence, the correct option is (2).

The correct answer is Newton's first law.

CONCEPT:

• Newton’s first law of motion: It is also called the law of inertia. Inertia is the ability of a body by virtue of which it opposes a change.
• According to Newton’s first law of motion, an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
• The inertia of rest: When a body is in rest, it will remain at rest until we apply an external force to move it. This property is called inertia of rest.
• The inertia of motion: When a body is in a uniform motion, it will remain in motion until we apply an external force to stop it. This property is called inertia of motion.

EXPLANATION:

• When a bus suddenly starts moving, the passengers fall backward due to the law of inertia of rest or 1st law of Newton.
• Because the body was in the state of rest and when the bus suddenly starts moving the lower body tends to be in motion, but the upper body still remains in a state of rest due to which it feels a jerk and falls backward. Hence option 1 is correct.

Additional Information

Laws of Motion given by Newton are as follows:

CONCEPT:

• Equation of motion: The mathematical equations used to find the final velocity, displacements, time, etc of a moving object without considering force acting on it are called equations of motion.
• These equations are only valid when the acceleration of the body is constant and they move on a straight line.
• 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.

EXPLANATION:

Given - Acceleration (a) = 2 m/s², Final velocity (v) = 30 m/s and Initial velocity (u) = 20 m/s

Displacement = s

We know,

⇒ v² - u² = 2as (Equation of Motion)

⇒ s = (v²- u²)/ (2 x a)

⇒ s = (30²-20²) / (2 x 2)

⇒ s = 500 /4

CONCEPT:

Work done:

It is the dot product of Force and Displacement.

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

Kinetic energy: 

The energy of a particle due to its velocity is called kinetic energy.

It is denoted by K.E.

\(K.E=\frac{1}{2}mV^2\)

where m = mass of the particle and V = velocity of the particle.

Work energy theorem:

The work done by all the forces on a system is equal to change in kinetic energy of the system.

Work done by all the forces (W) = Final K.E – Initial K.E

CALCULATION:

Given that:

Initial velocity (u) = 4 m/s, final velocity (v) = 8 m/s and

Mass (m) = 0.5 kg

Applying the work-energy theorem:

Work done = Change in Kinetic Energy:

ΔK.E = (K.E)₂ - (K.E)₁

\(\Rightarrow \frac{1}{2}m(v^2-u^2)\)

\(\Rightarrow \frac{1}{2}\times\;0.5\times(8^2-4^2)\)

∴ ΔK.E is 12 J

CONCEPT

• Equilibrium: It is a state where resultant of all forces acting on a body is zero.

• Stable equilibrium: A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement.

• The potential energy is minimum in this case.

• Unstable equilibrium: A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium.
  • The potential energy is maximum in this case.

• Neutral equilibrium: A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.
  • The potential energy remains constant in this case.

EXPLANATION

• If a ball is placed on vertical rod, it is in unstable equilibrium because once it is displaced from its place, it will experience the net force in the direction of displacement and never come back to its original position.
• The potential energy of the ball is maximum at this point.

∴ Option 2 is correct.

Concept:

Acceleration: 

• The rate of change of velocity is called the acceleration of the body. i.e.,\(a = \frac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}}\)
• Where V₂ = final velocity of the object, V₁ = initial velocity of the object, t₂ = final time, and t₁ = initial time
• It is a vector quantity.
• Its direction is the same as that of change in velocity (Not of the velocity).

Calculation:

Given - u = 18 km/h = 5 m/s v = 36 km/h = 10 m/s and t = 5 s

velocities in m/s would be 

u = 18 × 5/18 = 5 m/s and v = 36 ×5/18 = 10 m/s 

• As acceleration is written as
• \(\Rightarrow a = \frac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}} \)
• \(\Rightarrow a = \frac{{{10} - {5}}}{5}=1m/s^2 \)

Hence the correct answer is 1m/s²

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

• Odometer or odograph: It is a device used to measure the distance travelled by the vehicle.
• Speedometer or speed meter: A device used by the vehicle to measure the speed of the vehicle.
• Compass: A magnetic device used to find direction on the earth.

EXPLANATION

• As explained above odometer is used to measure the distance in automobiles. Therefore option 4 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 which after applying on a body changes or try to change the state of motion or state of rest is called force.
• Force is denoted by F and the SI unit is Newton (N).

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

CALCULATION

Given - Force (F) = 90 N and acceleration (a) = 2.6 m/s2

• The force required to accelerate a body of mass “m” with acceleration “a” is given by:

⇒ F = ma

⇒ 90  = m × 2.6

⇒ m = 90/2.6 

⇒ m  = 34.6 kg

CONCEPT:

• Newton’s first law of motion: It is also called the law of inertia. Inertia is the ability of a body by virtue of which it opposes a change.
• According to Newton’s first law of motion, an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
• The inertia of rest: When a body is in rest, it will remain at rest until we apply an external force to move it. This property is called inertia of rest.
• The inertia of motion: When a body is in a uniform motion, it will remain in motion until we apply an external force to stop it. This property is called inertia of motion.

EXPLANATION:

• The heavier the object is harder to move it or the greater the amount of force required to move it hence higher the inertia.
• Since higher mass has higher inertia. In all the above 4 options, a cricket ball has maximum mass so it will have maximum inertia. Hence option 4 is correct.