The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1. ${\tan }^{-1}(0.25)$
2. ${\tan }^{-1}(0.55)$
3. ${\tan }^{-1}(0.45)$
4. ${\tan }^{-1}(0.75)$

A body of mass \(m\) is kept on a rough horizontal surface (coefficient of friction =\(\mu)\). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by \(\vec F\) where:
1. \(|{\vec F}| = mg+\mu mg\)
2. \(|\vec F| =\mu mg\)
3. \(|\vec F| \le mg\sqrt{1+\mu^2}\)
4. \(|\vec F| = mg\)

A 5 m long uniformly thick string rests on a horizontal frictionless surface. It is pulled by a horizontal force of 5 N from one end. The tension in the string at 1 m from the end where the force is applied is:

A body of mass \(5\) kg is suspended by the strings making angles $60°$and $30°$with the horizontal.

Then:
a. ${\mathrm{T}}_1=25$ $\mathrm{N}$                    
b. ${\mathrm{T}}_2=25$ $\mathrm{N}$
c. ${\mathrm{T}}_1=25\sqrt{3}$ $\mathrm{N}$               
d. ${\mathrm{T}}_2=25\sqrt{3}$ $\mathrm{N}$
Choose the correct option:

A block is placed on a rough horizontal plane. A time dependent horizontal force, \(F=kt,\) acts on the block. The acceleration time graph of the block is :

1.		2.
3.		4.

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. The normal force on the motorcycle as it ascends the overbridge will be:

1.  increases.

2.  decreases.

3.  remains the same.

4.  fluctuates erratically.

Two masses, M and m, are attached to a vertical axis by weightless threads of combined length l. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity ω. If the tensions in the threads are the same during motion, the distance of M from the axis is:

1. $\frac{Ml}{M+m}$

2. $\frac{ml}{M+m}$

3. $\frac{M+m}{M}l$

4. $\frac{M+m}{m}l$

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 ms^–2)

A plank with a box on it at one end is gradually raised at the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank, respectively, will be:
    

A block of mass 1 kg lying on the floor is subjected to a horizontal force given by, \(F=2sin\omega t\) newtons. The coefficient of friction between the block and the floor is 0.25. The acceleration of the block will be:
1. positive and uniform
2. positive and non–uniform
3. zero
4. depending on the value of $\mathrm{\omega }$