A mass is performing a vertical circular motion (see figure.) If the average velocity of the particle is increased, then at which point the string will break?

     

1. A

2. B

3. C

4. D

If force \(F=500-100t,\) then the function of impulse with time will be:
1. \( 500 t-50 t^2 \)
2. \( 50 t-10 \)
3. \( 50-t^2 \)
4. \( 100 t^2\)
 

A man is slipping on a frictionless inclined plane & a bag falls down from the same height. Then the speed of both is related as:

1. V_B > V_m

2. V_B < V_m

3. V_B = V_m

4. V_B and V_m can't be related

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:

1. \(1. 65 \) m/s²
2. \(0.98 \) m/s²
3. \(1. 2 \) m/s²
4. \(0.25\) m/s²

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