A mass \(M\) of \(100~\text{kg}\) is suspended with the use of strings \(A\), \(B\) and \(C\) as shown in the figure. The tension in the string \(B\) will be:
           

1.	\(100 g~\text{N}\)	2.	zero
3.	\(100\sqrt{2}g~\text{N}\)	4.	\(\frac{100}{\sqrt{2}}g~\text{N}\)

Two masses, \(A\) and \(B\), each of mass \(M\) are fixed together by a massless spring. A force acts on the mass \(B\) as shown in the figure. If the mass \(B\) starts moving away from mass \(A\) with acceleration \(a\) in the ground frame, then the acceleration of mass \(A\) will be:

A \(40\) kg slab rests on a frictionless floor. A \(10\) kg block rests on top of the slab. The static coefficient of friction between the block and the slab is \(0.60\), while the kinetic coefficient of friction is \(0.40\). The \(10\) kg block is acted upon by a horizontal force of \(100\) N. If \(g =10 ~\text{m/s}^2,\) the resulting acceleration of the slab will be:

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is \(20\) m. The speed of the car at the top of the hill is between:
1. \(14~\text{m/s}~\text{and}~15~\text{m/s}\)
2. \(15~\text{m/s}~\text{and}~16~\text{m/s}\)
3. \(16~\text{m/s}~\text{and}~17~\text{m/s}\)
4. \(13~\text{m/s}~\text{and}~14~\text{m/s}\)

Three blocks with masses of \(m\), \(2m\), and \(3m\) are connected by strings as shown in the figure. After an upward force \(F\) is applied on block \(m\), the masses move upward at a constant speed, \(v\). What is the net force on the block of mass \(2m\)? (\(g\) is the acceleration due to gravity). 

            

1.	\(2mg\)	2.	\(3mg\)
3.	\(6mg\)	4.	zero

A monkey weighing \(20\) kg is holding a vertical rope. The rope will not break when a mass of \(25\) kg is suspended from it but will break if the mass exceeds \(25\) kg. What is the maximum acceleration with which the monkey can climb up the rope? (\(g = 10\) m/s²)
1. \(5\) m/s²
2. \(10\) m/s²
3. \(25\) m/s²
4. \(2.5\) m/s²

On the horizontal surface of a truck, a block of mass \(1\) kg is placed (\(\mu = 0.6\)) and the truck is moving with an acceleration of \(5\) m/s². The frictional force on the block will be:
1. \(5\) N
2. \(6\) N
3. \(5.88\) N
4. \(8\) N

An object of mass \(3\) kg is at rest. Now if a force of \(\overrightarrow{F} = 6 t^{2} \hat{i} + 4 t \hat{j}\) is applied to the object, then the velocity of the object at \(t =3\) second will be:
1. \(18 \hat{i} + 3 \hat{j}\)

2. \(18 \hat{i} + 6 \hat{j}\)

3. \(3 \hat{i} + 18 \hat{j}\)

4. \(18 \hat{i} + 4 \hat{j}\)

A rigid rod is placed against the wall as shown in the figure. When the velocity at its lower end is \(10\) ms^-1 and its base makes an angle \(\alpha=60^\circ\) with horizontal, then the vertical velocity of its end \(\mathrm{B}\) (in ms^-1) will be: