A balloon with mass \(m\) is descending down with an acceleration \(a\) (where \(a<g\)). How much mass should be removed from it so that it starts moving up with an acceleration \(a\)?

Three blocks with masses \(m\), \(2m\), and \(3m\) are connected by strings as shown in the figure. After an upward force \(F\) is applied on block \(m\), the masses move upward at constant speed \(v\). What is the net force on the block of mass \(2m\)? (\(g\) is the acceleration due to gravity)

           
1. \(2mg\)
2. \(3mg\)
3. \(6mg\)
4. zero

The mass of a lift is \(2000\) kg. When the tension in the supporting cable is \(28000\) N, then its acceleration is:
(Take \(g=10\) m/s²)

A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of ${\mathrm{30°}}^{\mathrm{}}$ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is:
              

1. 48 N

2. 24 N

3. 12 N

4. 96 N

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. \(mg~\mathrm{cos\theta}\)

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

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 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.  $\frac{15}{\sqrt{2}}m{s}^{-1}$