A car of mass 1000 kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is $45°$,the speed of the car is 

1. 20 $m{s}^{-1}$                                             2. 30 $m{s}^{-1}$

3. 5 $m{s}^{-1}$                                               4. 10 $m{s}^{-1}$

A car of mass m is moving on a level circular track of radius R. If ${\mathrm{\mu }}_{\mathrm{s}}$ represent the static friction between the road and tyres of the car, then the maximum speed of the car in circular motion is given by:

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration $1.0$ $\mathrm{m}/{\mathrm{s}}^2$. If $\mathrm{g}=10$ $\mathrm{m}/{\mathrm{s}}^2$, the tension in the supporting cable is:

1. 9680 N

2. 11000 N

3. 1200 N

4. 8600 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) 1.5 Mv                                                 

(2) 2 Mv

(3) zero                                                     

(4) Mv

A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is $\mathrm{\mu }=0.5.$ The distance that the box will move relative to the belt before coming to rest on it taking $\mathrm{g}=10 {\mathrm{ms}}^{-2}$, is 

1. $1.2 \mathrm{m}$                                            2. $0.6 \mathrm{m}$

3. zero                                               4. $0.4 \mathrm{m}$

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 $\alpha$ of the cart that will prevent the block from falling satisfies

1. $\alpha >\frac{mg}{\mu }$                                       2. $\alpha >\frac{g}{\mu m}$

3. $\alpha \ge \frac{g}{\mu }$                                          4. $\alpha <\frac{g}{\mu }$

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, its acceleration is:

(a) $30 {\mathrm{ms}}^{-2} \mathrm{downwards}$                                      (b) $4 {\mathrm{ms}}^{-2} \mathrm{upwards}$

(c) $4 {\mathrm{ms}}^{-2} \mathrm{downwards}$                                        (d) $14 {\mathrm{ms}}^{-2} \mathrm{upwards}$

A body, under the action of a force $\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k},$ acquires an acceleration of 1$m{s}^{-2}.$ The mass of this body must be

(1) $20\sqrt{10}kg$                                   

(2) 10kg

(3) 20kg                                         

(4) $10\sqrt{2}kg$                                

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20m. The speed of the car at the top of the hill is between:

1. 14m/s and 15m/s

2. 15m/s and 16m/s

3. 16m/s and 17m/s

4. 13m/s and 14m/s