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

1. \(60\) N
2. \(40\) N
3. \(50\) N
4. \(80\) N

A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity $\mathrm{v} = (5\mathrm{t} \hat{\mathrm{i}} + 2\mathrm{t} \hat{j})$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/s${}^2$)

$1. \sqrt{29} \mathrm{N}$
$2. 29 \mathrm{N}$
$3. 26 \mathrm{N}$
$4. \sqrt{89} \mathrm{N}$
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Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to block of mass M as shown in the fig. The magnitude of force P is

1. (M + m) g tan $\mathrm{\beta }$

2. g tan $\mathrm{\beta }$

3. (M + m) g cosec $\mathrm{\beta }$

4. mg cos $\mathrm{\beta }$

All surface shown in figure are smooth. System is released with the spring unstretched. In equilibrium, compression in the spring will be:

1. $\frac{2mg}{k}$

2. $\frac{\left(M+m\right)g}{\sqrt{2}k}$

3. $\frac{mg}{\sqrt{2}k}$

4. $\frac{mg}{k}$

Figure shows two blocks, each of mass m. The system is released form rest. If accelerations of blocks A and B at any instant (not initially) are ${\mathrm{a}}_1$ and ${\mathrm{a}}_2$, respectively, then

1. ${\mathrm{a}}_1={\mathrm{a}}_2\mathrm{cos\theta }$

2. ${\mathrm{a}}_2={\mathrm{a}}_1\mathrm{cos\theta }$

3. ${\mathrm{a}}_1={\mathrm{a}}_2$

4. None of these

A trolley A has a simple pendulum suspended from a fixed to its desk. A block B is in contact on its vertical side. The trolley is on horizontal rails and accelerates towards the right such that the block is just prevented from falling. The value of the coefficient of friction between A and B is 0.5. The inclination of the pendulum to the vertical is

1. ${\tan }^{-1}\left(\frac{1}{2}\right)$

2. ${\tan }^{-1}\left(3\right)$

3. ${\tan }^{-1}\left(\sqrt{2}\right)$

4. ${\tan }^{-1}\left(2\right)$

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: 

1. g downward

2. g upward

3. more than g downward

4. zero

Two bodies of mass, \(4~\text{kg}\) and \(6~\text{kg}\), 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:

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:

1. \(2.5\) kg-m/s

2. \(5\) kg-m/s

3. \(0.05\) kg-m/s

4. \(25\) kg-m/s

A 0.5 kg body experiences a force \(F=(2+3x^2)\) 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: