A particle of mass m is tied to a string of length \(l\) and whirled into a horizontal plane. If the tension in the string is T, then the speed of the particle will be:

1. $\sqrt{\frac{Tl}{m}}$

2. $\sqrt{\frac{2Tl}{m}}$

3. $\sqrt{\frac{3Tl}{m}}$

4. $\sqrt{\frac{T}{ml}}$

A small ball is suspended from a thread. If it is lifted up with an acceleration of \(4.9\) ms^–2 and lowered with an acceleration of \(4.9\) ms^–2, then the ratio of the tension in the thread in both cases will be:
1. \(1:3\)
2. \(3:1\)
3. \(1:1\)
4. \(1:5\)

If a ladder is not in a balanced condition against a smooth vertical wall, then it can be brought to a balanced condition by:

For rocket propulsion, the velocity of exhaust gases relative to the rocket is \(2\) km/s. If the mass of a rocket system is \(1000\) kg, then the rate of fuel consumption for the rocket to rise up with an acceleration \(4.9\) m/s² will be:
1. \(12.25\) kg/s
2. \(17.5\) kg/s
3. \(7.35\) kg/s
4. \(5.2\) kg/s

A rigid rod is placed against the wall as shown in the figure. When the velocity at its lower end is \(10\) ms^-1 and its base makes an angle \(\alpha=60^\circ\) with horizontal, then the vertical velocity of its end \(\mathrm{B}\) (in ms^-1) will be:
                  

If \(100\) N force is applied to \(10\) kg block as shown in diagram, then the acceleration produced for the slab will be:

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

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