Definition of Force Inertia and First Law

Practice Questions:

Question 11: easy

An object of mass 2 kg is placed on a smooth horizontal surface. A water jet throws water at a rate of 2 kg/s with speed 20 m/s which strikes the object horizontally. The force applied by water jet and acceleration of the object respectively, are

1. \[20 N, 40 m/s^2\]

2. \[40 N, 20 m/s^2\]

3. Zero, zero

4. \[12 N, 12 m/s^2\]

View Answer

Formula: \(F = v \frac{dm}{dt} = 20 \times 2 = 40\text{ N}\). Using Newton's second law, acceleration \(a = \frac{F}{m} = \frac{40}{2} = 20\text{ m/s}^2\).

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Question 12: easy

A player catches a ball of mass \(150\text{ g}\) in \(0.1\text{ s}\) moving with speed \(20\text{ m/s}\), then he experiences an average force of

1. \(300\text{ N}\)

2. \(30\text{ N}\)

3. \(3\text{ N}\)

4. \(0.3\text{ N}\)

View Answer

By Newton's second law, \(F = \frac{\Delta p}{\Delta t} = \frac{mv}{t}\). Substituting the values, \(F = \frac{0.15\text{ kg} \times 20\text{ m/s}}{0.1\text{ s}} = 30\text{ N}\).

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Question 13: easy

If a cloth covers a table and some dishes are kept on it, then the cloth can be pulled out without dislodging the dishes from the table by pulling the cloth suddenly. The dishes will remain on table due to

1. Work-energy theorem

2. For every action, there is an equal and opposite reaction

3. Inertia of motion

4. Inertia of rest

View Answer

According to Newton's First Law, when the cloth is suddenly pulled, the dishes tend to maintain their state of rest due to the inertia of rest.

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Question 14: easy

Assertion (A): If a particle is found to be in equilibrium in two different frames of reference implies that both frames are inertial.

Reason (R): Newton’s second law can be used for motion of a particle in any reference frame.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

Assertion (A) is false. Two non-inertial frames accelerating identically relative to an inertial frame could both observe a particle in equilibrium. Reason (R) is false. Newton's second law \( \vec{F} = m \vec{a} \) strictly applies in inertial frames; pseudo forces must be included in non-inertial frames. Therefore, both (A) and (R) are false.

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Question 15: easy

Read the statements marked as assertion (A) and reason (R) and choose the correct option.

Assertion (A): If no external force acts on a system, the velocity of the centre of mass remains constant.

Reason (R): If there is no external force on system, then momentum of system is conserved.

1. Both (A) and (R) are true and (R) is the correct explanation of (A)

2. Both (A) and (R) are true but (R) is not the correct explanation of (A)

3. (A) is true but (R) is false

4. (A) is false but (R) is true

View Answer

When no external force acts on the system, the acceleration of the center of mass is zero, hence its velocity is constant. This also implies the conservation of total linear momentum of the system.

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Question 16: easy

1. Work-energy theorem

2. For every action, there is an equal and opposite reaction

3. Inertia of motion

4. Inertia of rest

View Answer

According to Newton's first law of motion, the dishes tend to remain at rest due to their inertia of rest when the cloth is suddenly pulled.

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