A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by:
                 

1. $\sqrt{2}Mg$

2. $\sqrt{2}mg$

3. $\sqrt{{(M+m)}^2+m^2}g$

4.$\sqrt{{(M+m)}^2+M^2}g$

The variation of momentum with the time of one of the bodies in a two-body collision is shown in fig. The instantaneous force is the maximum corresponding to the point:
      
1. P

2. Q

3. R

4. S

A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q inclined at an angle θ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is: 

1. $\frac{(P+Q\sin \theta )}{(mg+Q\cos \theta )}$

2. $\frac{(P\cos \theta +Q)}{(mg-Q\sin \theta )}$

3. $\frac{(P+Q\cos \theta )}{(mg+Q\sin \theta )}$

4. $\frac{(P\sin \theta -Q)}{(mg-Q\cos \theta )}$

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be: 
     
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

A particle moves in the XY-plane under the action of a force F such that the components of its linear momentum p at any time t are \(p_x = 2 \cos t\),  \(p_y = 2 \sin t\) . The angle between F and p at time t will be:

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ and the lighter one in the radius r. The tangential speed of lighter stone is n times that of heavier stone when they experience the same centripetal forces. The value of n is:

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 ball of mass 0.1 Kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 rpm. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:

 The length of a spring is  \(l_1\) and \(l_2\) when stretched with a force of 4 N and 5 N respectively. Its natural length is?

A rigid ball of mass \(M\) strikes a rigid wall at \(60^{\circ}\) and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be: