A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first \(2\) s, it rotates through an angle \(\theta_1\). In the next \(2\) s, it rotates through an additional angle \(\theta_2\). The ratio of \(\frac{\theta_2}{\theta_1}\) is: 
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

A particle of mass m moving with velocity u makes an elastic one-dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F₀ linearly in time T/2 and decreases linearly to zero in further time T/2. The magnitude of F₀ is:

1. mu/T

2. 2mu/T

3. mu/2T

4. None of these

A force of 50 dynes is acted on a body of mass 5 g which acts for an interval of 3 seconds, then impulse is 

1. 0.15 × 10^–3 N-s

2. 0.98 × 10^–3 N-s

3. 1.5 × 10^–3 N-s

4. 2.5 × 10^–3 N-s

In an explosion a body breaks up into two pieces of unequal masses. In this 

(1) Both parts will have numerically equal momentum

(2) Lighter part will have more momentum

(3) Heavier part will have more momentum

(4) Both parts will have equal kinetic energy

Two bodies of masses m₁ and m₂ have equal kinetic energies. If p₁ and p₂ are their respective momentum, then ratio p₁ : p₂ is equal to 

(1) $m_1:m_2$

(2) $m_2:m_1$

(3) $\sqrt{m_1}:\sqrt{m_2}$

(4) $m_1^2:m_2^2$

A light and a heavy body have equal momenta. Which one has greater K.E 

(1) The light body

(2) The heavy body

(3) The K.E. are equal

(4) Data is incomplete

If the K.E. of a body is increased by 300%, its momentum will increase by 

(1) 100%

(2) 150%

(3) $\sqrt{300}\%$

(4) 175%

A light and a heavy body have equal kinetic energy. Which one has a greater momentum ? 

(1) The light body

(2) The heavy body

(3) Both have equal momentum

(4) It is not possible to say anything without additional information

Two bodies with kinetic energies in the ratio of 4 : 1 are moving with equal linear momentum. The ratio of their masses is 

(1) 1 : 2

(2) 1 : 1

(3) 4 : 1

(4) 1 : 4

In uniform circular motion

1. Both the angular velocity and the angular momentum vary

2. The angular velocity varies but the angular momentum remains constant

3. Both the angular velocity and the angular momentum stay constant

4. The angular momentum varies but the angular velocity remains constant