The linear momentum p of a body moving in one dimension varies with time according to the equation p = a + bt² where a and b are positive constants. The net force acting on the body is 

(1) A constant

(2) Proportional to t²

(3) Inversely proportional to t

(4) Proportional to t

A block \(A\) of mass \(7\) kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body \(B\) of mass \(3\) kg at the other end. The acceleration of the system will be: (given \(g=10~\text{m/s}^2)\)

A body of weight 2kg is suspended as shown in the figure. The tension T₁ in the horizontal string (in kg wt) is 

(1) $2/\sqrt{3}$

(2) $\sqrt{3}/2$

(3) $2\sqrt{3}$

(4) 2

Two masses m₁ = 5 kg and m₂ = 4.8 kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when they are free to move (g = 9.8 m/s²) 

(1) 0.2 m/s²

(2) 9.8 m/s²

(3) 5 m/s²

(4) 4.8 m/s²

A block of mass 4 kg is suspended through two light spring balances A and B. Then A and B will read respectively:

(1) 4 kg and zero kg

(2) Zero kg and 4 kg

(3) 4 kg and 4 kg

(4) 2 kg and 2 kg

The mass of a body measured by a physical balance in a lift at rest is found to be m. If the lift is going up with an acceleration a, its mass will be measured as:

1. $m\left(1-\frac{{\displaystyle a}}{{\displaystyle g}}\right)$

2. $m\left(1+\frac{{\displaystyle a}}{{\displaystyle g}}\right)$

3. m

4. Zero

In the arrangement shown in figure, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed 

1. $2U \cos \theta$

2. $U \cos \theta$

3. $\frac{2U}{\cos \theta }$

4. $\frac{U}{\cos \theta }$

A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity $v=(5t\hat{i}+2t\hat{j})m/s$. Here t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take g = 10 m/s²)

1. $\sqrt{29}N$

2. 29 N

3. 26 N

4. $\sqrt{89}N$

The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration 12 m/sec². What is the acceleration of 20 kg mass?

(1) 12 m/sec²

(2) 4 m/sec²

(3) 10 m/sec²

(4) Zero

The blocks A and B are arranged as shown in the figure. The pulley is frictionless. The mass of A is 10 kg. The coefficient of friction of A with the horizontal surface is 0.20. The minimum mass of B to start the motion will be 

(1) 2 kg

(2) 0.2 kg

(3) 5 kg

(4) 10 kg