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?
   $\mathrm{}$

1.	\(\overrightarrow N+\overrightarrow T+\overrightarrow W=0\)	2.	\(T^2=N^2+W^2\)
3.	\(T = N + W\)	4.	\(N = W \tan \theta\)

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 \(1~\text{m/s}^2\), then the reaction of the floor of the lift on the man will be: \(\left(g = 9.8~\text{m/s}^2 \right)\)

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 \(F\text-t\) graph is given.

Consider the following statements.

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. $\frac{\mathrm{r}}{4}$

A massless string of length 1 m fixed at one end carries a mass of 2 kg at the other end. The string makes $\frac{2}{\mathrm{\pi }}$ rev/s around the axis through the fixed end as shown in the figure. The tension on the string will be:
            

Three blocks A, B and C of mass 3M, 2M and M respectively are suspended vertically with the help of springs PQ and TU and a string RS as shown in fig. The acceleration of blocks A, B and C are $a_1,a_2 and a_3$ respectively.
     

The value of acceleration \(a_{1}\) at the moment string RS is cut will be: 

1. g downward

2. g upward

3. more than g downward

4. zero

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