The angle of banking for a cyclist taking a turn at a curve is given by tan$\mathrm{\theta } = \frac{{\mathrm{v}}^{\mathrm{n}}}{\mathrm{rg}}$ where symbols have their usual meaning. The value of n is:

1.	1	2.	2
3.	3	4.	4

 

The maximum constant speed with which a car can move on a flat horizontal circular road with the radius of curvature 20 m and a coefficient of static friction 0.5 is: (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

A 100 kg gun fires a ball of 1 kg horizontally from a cliff at a height of 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is: (Take g = 10 m/s²)

1. 0.2 m/s

2. 0.4 m/s

3. 0.6 m/s

4. 0.8 m/s

A metal sphere is suspended from a wall by a string. The forces acting on the sphere are shown in the figure. Which of the following statements is NOT correct?
   $\mathrm{}$

Calculate the reading of the spring balance shown in the figure: (take \(g=10\) m/s²)
                

1. \(60\) N
2. \(40\) N
3. \(50\) N
4. \(80\) N

In the diagram, a 100 kg block is moving up with constant velocity. Find out the tension at point P.

1. 1330 N

2. 490 N

3. 1470 N

4. 980 N

If a young man of mass 60 kg stands on the floor of a lift which is accelerating downwards at 1 $\mathrm{m}/{\mathrm{s}}^2$, then the reaction of the floor of the lift on the man will be: (g=9.8$\mathrm{m}/{\mathrm{s}}^2$)

If $\mathrm{\mu }$ between block A and inclined plane is 0.5 and that between block B and the inclined plane is 0.8, then the normal reaction between blocks A and B will be:
                     
1. 180 N

2. 216 N

3. 0

4. None of these

A particle is on a smooth horizontal plane. A force F is applied, whose F-t graph is given.

Consider the following statements.
a. At time ${\mathrm{t}}_1$, acceleration is constant.
b. Initially the particle must be at rest.
c. At time ${\mathrm{t}}_2$, acceleration is constant.
d. The initial acceleration is zero.
Select the correct statement(s):

A coin placed on a rotating table just slips if it is placed at a distance 4r from the center. On doubling the angular velocity of the table, the coin will just slip when the distance from the centre is equal to:-

1. 4r

2. 2r

3. r

4. $\frac{\mathrm{r}}{4}$