The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time. Its

(a) velocity remains constant

(b) speed remains constant

(c) acceleration remains constant

(d) tangential acceleration remains constant

Choose the correct option:

1. (a) and (d)

2. (b) and (d)

3. (c) and (d)

4. (a) and (c)

A particle is going in a spiral path as shown in the figure with constant speed.

A car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a.

(a) The acceleration of the car is towards the centre of the path

(b) The magnitude of the frictional force on the car is greater than \(\frac{mv^2}{r}\)

(c) The friction coefficient between the ground and the car is not less than a/g

(d) The friction coefficient between the ground and the car is µ = tan^–1 \(\frac{v^2}{rg}\)

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

A circular road of radius r is banked for a speed v = 40 km/hr. A car of mass m attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible.

(a) The car cannot make a turn without skidding

(b) If the car turns at a speed less than 40 km/hr, it will slip down

(c) If the car turns at the correct speed of 40 km/hr, the force by the road on the car is equal to \(\frac{mv^2}{r}\)

(d) If the car turns at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than \(\frac{mv^2}{r}\)

Choose the correct option:

1. (b) and (d)

2. (c) and (d)

3. (a) and (d)

4. (a), (b) and (c)

A person applies a constant force \(\overrightarrow F\) on a particle of mass m and finds that the particle moves in a circle of radius r with a uniform speed v as seen from an inertial frame of reference.

(a) This is not possible

(b) There are other forces on the particle

(c) The resultant of the other forces is \(\frac{mv^2}{r}\) towards the centre

(d) The resultant of the other forces varies in magnitude as well as in direction

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. (b) and (d)

Consider the following two statements 

Internal forces can change:

A nucleus moving with a velocity \(\overrightarrow v\) emits an \(\alpha\)-particle. Let the velocities of the α-particle and the remaining nucleus be \(\overrightarrow {v_1}\) and \(\overrightarrow {v_2}\) and their masses be \(m_1\) and \(m_2\).
 

A shell is fired from a cannon with a velocity V at an angle θ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the canon. The speed of the other piece immediately after the explosion is:

1. 3V cosθ

2. 2V cosθ

3. \(\frac{3}{2}\)V cosθ

4. V cosθ

One end of a uniform rod of mass m and length I is clamped. The rod lies on a smooth horizontal surface and rotates on it about the clamped end at a uniform angular velocity ω. The force exerted by the clamp on the rod has a horizontal component:

1. mω²l

2. zero

3. mg

4. \(\frac{1}{2}mω^2l\)