The coefficient of static friction, \(\mu_s,\) between block A of mass \(2\) kg and the table as shown in the figure is \(0.2\). What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless. (Take \(g=10\) m/s² ) 

      

1. \(4.0\) kg
2. \(0.2\) kg
3. \(0.4\) kg
4. \(2.0\) kg

An object of mass \(3\) kg is at rest. Now if a force of \(\overrightarrow{F} = 6 t^{2} \hat{i} + 4 t \hat{j}\) is applied to the object, then the velocity of the object at \(t =3\) second will be:
1. \(18 \hat{i} + 3 \hat{j}\)

2. \(18 \hat{i} + 6 \hat{j}\)

3. \(3 \hat{i} + 18 \hat{j}\)

4. \(18 \hat{i} + 4 \hat{j}\)

A block of mass 10 kg is placed on a rough horizontal surface with a coefficient of friction µ = 0.5. If a horizontal force of 100 N acts on the block, then the acceleration of the block will be: 

1. 10 m/s²

2. 5 m/s²

3. 15 m/s²

4. 0.5 m/s²

If a lift of mass 1000 Kg is moving with an acceleration of 1 m/s² in an upward direction, then the tension developed in the string that is connected to the lift is: 

1. 9800 N

2. 10, 800 N

3. 11000 N

4. 10, 000 N

A cricketer catches a ball of mass \(150~\mathrm{gm}\) in \(0.1\) \(\mathrm{s}\) moving with a speed of \(20~\mathrm{ms^{-1}}\). Then he experiences a force of:
1. \(300~\mathrm{N}\)
2. \(30~\mathrm{N}\)
3. \(3~\mathrm{N}\)
4. \(0.3~\mathrm{N}\)

On the horizontal surface of a truck, a block of mass \(1\) kg is placed (\(\mu = 0.6\)) and the truck is moving with an acceleration of \(5\) m/s². The frictional force on the block will be:
1. \(5\) N
2. \(6\) N
3. \(5.88\) N
4. \(8\) N

A monkey weighing \(20\) kg is holding a vertical rope. The rope will not break when a mass of \(25\) kg is suspended from it but will break if the mass exceeds \(25\) kg. What is the maximum acceleration with which the monkey can climb up the rope? (\(g = 10\) m/s²)
1. \(5\) m/s²
2. \(10\) m/s²
3. \(25\) m/s²
4. \(2.5\) m/s²

A man weighs 80 kg. He stands on a weighing scale in a lift that is moving upwards with a uniform acceleration of 5m/s². What would be the reading on the scale? (g = 10 m/s²)

1. Zero

2. 400 N

3. 800 N

4. 1200 N

A 1 kg stationary bomb explodes in three parts having mass 1 : 1 : 3 respectively. If parts having the same mass move in a perpendicular direction with a velocity of 30 m$s^{-1}$, then the velocity of the bigger part will be: 

1.  $10$ $\sqrt{2}$ $m{s}^{-1}$

2. $\frac{10}{\sqrt{2}}m{s}^{-1}$

3. $15$ $\sqrt{2}$ $m{s}^{-1}$

4.  $\frac{15}{\sqrt{2}}m{s}^{-1}$

A block of mass \(m\) is placed on a smooth wedge of inclination \(\theta\). The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (\(g\) is the acceleration due to gravity) will be:
1. \(mg~\mathrm{sin\theta}\)
2. \(mg\)
3. \(\frac{mg}{\mathrm{cos\theta}}\)
4. \(mg~\mathrm{cos\theta}\)