Which of the following sets of concurrent forces may be in equilibrium?

Two blocks A and B are connected by a light string as shown in the figure. The force exerted by the string on the block B is:

A rod of mass m length l is moving between perpendicular smooth walls as shown. When the rod is at an angle $\mathrm{\theta }$ with horizontal its end A is moving right with speed v. The speed of end B is

The figure shows a rod of length 5 m. Its ends, A and B, are restrained to moving in horizontal and vertical guides. When the end A is 3 m above O, it moves at 4 m/s. The velocity of end B at that instant is:
         

A rod supported on the wall starts slipping down. If the speed ${\mathrm{v}}_{\mathrm{A}}$ of upper-end A is 5 m/s, then the speed ${\mathrm{v}}_{\mathrm{B}}$ with which end B will move to the left, as shown in the figure, is

If the block is being pulled by the rope moving at speed v as shown, then the horizontal velocity of the block is:

In the given figure, spring balance is massless, so the reading of spring balance will be:
                     

The strings and pulleys shown in the figure are massless. The reading shown by the light spring balance S is:

In the figure shown the horizontal surface is smooth and the strings are inextensible and the massless pulleys are light. If the acceleration of block 1 kg is a, then acceleration of 3 kg is:

What is velocity of the block when the angle between string and horizontal is 30° as shown in the diagram?

A ball of mass 1 kg projected with velocity 20 m/s from the origin of an XY coordinate axes at an angle 30° with horizontal. The change in momentum in 1 s is:

In the following questions, a statement of assertion (A) is followed by a statement of the reason (R).

A: A safe turn by a cyclist should neither be too fast nor too sharp.

R: This is so because it increases the chances of skidding.

A motorcyclist is maintaining constant speed while going on an overbridge of radius R. When the motorcycle is ascending on the overbridge, the normal reaction on it

A bucket full of water tied with the help of a 2 m long string performs a vertical circular motion. The minimum angular velocity of the bucket at the uppermost point so that water will not fall will be:

A mass of 4 kg is suspended as shown in the figure with the help of massless inextensible string A. Another identical string, B, is connected at the lower end of the block. When a sudden pulling downward jerk slightly greater than the breaking strength of A and B is given to string B, then:
                           

A 0.5 kg body experiences a force F = (2 + 3x²) N, where x in metres is the displacement from the origin. If it is released to move along the X-axis from the origin, then its initial acceleration is:

On the application of an impulsive force, a sphere of mass \(500\) g starts moving with an acceleration of \(10\) m/s². The force acts on it for \(0.5\) s. The gain in the momentum of the sphere will be:

Calculate the reading of the spring balance shown in figure:- (g = 10 m/s²)
                      

Three blocks A, B and C of mass 3M, 2M and M respectively are suspended vertically with the help of springs PQ and TU and a string RS as shown in fig. The acceleration of blocks A, B and C are $a_1,a_2 and a_3$ respectively.
     

The value of acceleration \(a_{1}\) at the moment string RS is cut will be: 

Two bodies of mass, 4 kg and 6 kg, are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is:

Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is 0.05. (g = 10 m/${\mathrm{s}}^2$, the mass of the string is negligible and no other friction exists).

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Figure. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with $2 m s^{-2}$. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?

A rocket with a lift-off mass of 20,000 kg is blasted upwards with an initial acceleration of $5 m s^{-2}$. Then initial thrust (force) of the blast is:

$$\begin{gathered} 1. 7\times {10}^5 N \\ 2. 0 \\ 3. 2\times {10}^5 N \\ 4. 3\times {10}^5 N \end{gathered}$$

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. The acceleration of the masses and the tension in the string when the masses are released are:

$$\begin{gathered} 1. 2 m{s}^{-2}, 69 N \\ 2. 1 m{s}^{-2}, 69 N \\ 3. 2 m{s}^{-2}, 96 N \\ 4. 1 m{s}^{-2}, 96 N \end{gathered}$$

A batsman deflects a ball of mass 0.15 kg by an angle of 45° without changing its initial speed which is equal to 54 km/h. Then impulse imparted to the ball is:

$$\begin{gathered} \left(1\right) 5.2 kgm{s}^{-1} \\ \left(2\right) 3.2 kgm{s}^{-1} \\ \left(3\right) 2.2 kgm{s}^{-1} \\ \left(4\right) 4.2 kgm{s}^{-1} \end{gathered}$$

The figure shows the position-time graph of a body of mass 0.04 kg. Then the magnitude of each impulse is:

$$\begin{gathered} \left(1\right) 8\times {10}^{-4} kg m{s}^{-1} \\ \left(2\right) 8\times {10}^{-3} kg m{s}^{-1} \\ \left(3\right) 4\times {10}^{-4} kg m{s}^{-1} \\ \left(4\right) 4\times {10}^{-3} kg m{s}^{-1} \end{gathered}$$

A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 m/s. How long does the body take to stop?

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m/s to 3.5 m/s in 25 sec. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?

A body of mass 5 kgis acted upon by two perpendicular forces, 8 N and 6 N. The magnitude of the acceleration of the body is: