A person of mass \(60\) kg is inside a lift of mass \(940\) kg and presses the button on the control panel. The lift starts moving upwards with an acceleration of \(1.0~\text{ms}^{-2}\)${\mathrm{}}^{}$. If \(g=10~\text{ms}^{-2}\)${\mathrm{}}^{}$, the tension in the supporting cable is:
1. \(9680~\text{N}\)
2. \(11000~\text{N}\)
3. \(1200~\text{N}\)
4. \(8600~\text{N}\)

A body of mass \(M\) hits normally a rigid wall with velocity \(v\) and bounces back with the same velocity. The impulse experienced by the body is:
1.  \(1.5Mv\)
2. \(2Mv\)
3. zero
4. \(Mv\)

A block of mass \(m\) is in contact with the cart \((C)\) as shown in the figure. 
                    
The coefficient of static friction between the block and the cart is \(\mu.\) The acceleration \(a\) of the cart that will prevent the block from falling satisfies:
1. \(a > \dfrac{mg}{\mu}\)
2. \(a > \dfrac{g}{\mu m}\)
3. \(a \ge \dfrac{g}{\mu}\)
4. \(a < \dfrac{g}{\mu}\)

A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if:

1. $r=\mu g{\omega }^2$

2. $r<\frac{{\omega }^2}{\mu g}$

3. $r\le \frac{\mu g}{{\omega }^2}$

4. $r\ge \frac{\mu g}{{\omega }^2}$

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 body, under the action of a force \(\overset{\rightarrow}{F} = 6 \hat{i} - 8 \hat{j} + 10 \hat{k}\), acquires an acceleration of 1 ms^-2. The mass of this body must be:

1. 2 √10 kg

2. 10 kg

3. 20 kg

4. 10 √2 kg

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be:
1.  Mv Newton

2.  2Mv Newton

3.  $\frac{\mathrm{Mv}}{2}$ Newton

4.  zero

A block \(B\) is pushed momentarily along a horizontal surface with an initial velocity \(v.\) If \(\mu\) is the coefficient of sliding friction between \(B\) and the surface, the block \(B\) will come to rest after a time: 
 
1. \(v \over g \mu\)
2. \(g \mu \over v\)
3. \(g \over v\)
4. \(v \over g\)

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