The value of \(M\) of the hanging block is in the figure, which will prevent the smaller block (\(m\)\(=\)\(1\) kg) from slipping over the triangular block. All the surfaces are smooth and string and pulley are ideal. (Given: \(M'\)\(=4\) kg and \(\theta\) \(=37^\circ\))

           
1. \(12\) kg
2. \(15\) kg
3. \(10\) kg
4. \(4\) kg

A plumb line is suspended from a ceiling of a car moving with horizontal acceleration of a. What will be the angle of inclination with vertical 

1. tan^–1(a/g)

2. tan^–1(g/a)

3. cos^–1(a/g)

4. cos^–1(g/a)

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be 

1. $mg<mspace\; width="1em"></mspace>\cos \theta$

2. $mg<mspace\; width="1em"></mspace>\sin \theta$

3. mg

4. $mg/\cos \theta$

A block is kept on a frictionless inclined surface with an angle of inclination 'α'. The incline is given an acceleration 'a' to keep the block stationary. Then a is equal to 

1. g

2. gtanα

3. g/tanα

4. gcosecα

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. \( m\left (1-\dfrac{a}{g} \right )\)
2. \( m\left (1+\dfrac{a}{g} \right )\)
3. \(m\)
4. zero

On the horizontal surface of a truck (μ = 0.6), a block of mass 1 kg is placed. If the truck is accelerating at the rate of 5m/sec² then frictional force on the block will be 

1. 5 N

2. 6 N

3. 5.88 N

4. 8 N

A block of mass m is in contact with the cart C as shown in the figure.

The coefficient of static friction between the block and the cart is $\mu .$The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies

1. $\alpha >\frac{mg}{\mu }$                                       2. $\alpha >\frac{g}{\mu m}$

3. $\alpha \ge \frac{g}{\mu }$                                          4. $\alpha <\frac{g}{\mu }$

A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\mathrm{\theta }$ with the vertical

1. ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the forward direction

2. ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the upward direction 

3. ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the backward direction

4. ${\tan }^{-1}\left(\frac{g}{a}\right)$ in the forward directions 

A pendulum bob is suspended in a Car moving horizontally with acceleration ‘a’ the angle the string will make with vertical is

1. ${\tan }^{-1}\frac{g}{a}$

2. ${\tan }^{-1}\frac{a}{g}$

3. $si{n}^{-1}\frac{a}{g}$

4. ${\cos }^{-1}\frac{a}{g}$

A block of mass $m$ is placed on the floor of lift which is moving with velocity $v$ = $4t^2$, where $t$ is time in second and velocity  m/s. Find the time at which normal force on the block is three times of its weight.

1. (3g/8)s

2. g s

3. g/4 s

4. 3g s