A block of mass \(m\) slides down a smooth plane inclined at an angle of \(60^\circ\) with the horizontal. The normal reaction of the incline acting on the block equals:

1.	\(mg\sin60^\circ\)	2.	\(mg\cos60^\circ\)
3.	\(mg\tan60^\circ\)	4.	\(mg\cot60^\circ\)

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 from the given ones:

1. (a) and (d)

2. (b) and (d)

3. (c) and (d)

4. (a) and (c)

An object follows a curved (circular) path. The following quantities may remain constant during the motion.

Choose the correct option from the options given below:

Two cars having masses \(m_1\) and \(m_2\) move in circles of radii \(r_1\) and \(r_2\) respectively. If they complete the circles in equal time, the ratio of their angular speeds \(\dfrac{\omega_1}{\omega_2}\) is:
1. \(\dfrac{m_1}{m_2}\)

2. \(\dfrac{r_1}{r_2}\)

3. \(\dfrac{m_1r_1}{m_2r_2}\)

4. \(1\)

A person reports that a particle has a non-zero acceleration even though no force is acting on it. Which of the following could explain this observation?

If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be:

 
Choose the correct option:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. all of the above

The figures show the displacement of a particle going along the \(x\text-\)axis as a function of time. The force acting on the particle is zero in the region:

Choose the correct option from the given ones: