A body of mass 5 kg is acted upon by two perpendicular forces, 8 N and 6 N. The magnitude of the acceleration of the body is:

1.	0.99 ms-2	2.	3 ms-2
3.	2 ms-2	4.	0.77 ms-2

A stone of mass \(\mathrm{m}\) tied to the end of a string revolves in a vertical circle of radius \(\mathrm{R}.\) The net forces at the lowest and highest points of the circle directed vertically downwards are:

(${\mathrm{T}}_1$ and ${\mathrm{v}}_1$ denote the tension and speed at the lowest point.${\mathrm{T}}_2$ and ${\mathrm{v}}_2$ denote corresponding values at the highest point.)

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1. inclined at a 60$°$ angle from vertical

2. the mass is at the highest point

2. the wire is horizontal

4. the mass is at the lowest point.

A point mass 'm' is moved in a vertical circle of radius 'r' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point will be:

1. 6 mg

2. 7 mg

3. 8 mg

4. 1 mg

A string tied on a roof bears a maximum tension of 50 kg-wt. The minimum acceleration that can be acquired by a man of 98 kg to descend will be:
[Take g=9.8 m/s²]

1. 9.8 m/s²

2. 4.9 m/s²

3. 4.8 m/s²

4. 5 m/s²

As shown in the figure, two masses of 10 kg and 20 kg, respectively are connected by a massless spring. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has an acceleration of 12 m/s² towards the right. The acceleration of 20 kg mass at this instant is:
        
1. 12 m/s² 

2. 4 m/s² 

3. 10 m/s² 

4. Zero

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. The acceleration of the masses and the tension in the string when the masses are released are:

$1.$ $$ $2$ $m{s}^{-2},$ $69$ $N$
$2.$ $$ $1$ $m{s}^{-2},$ $69$ $N$
$3.$ $$ $2$ $m{s}^{-2},$ $96$ $N$
$4.$ $$ $1$ $m{s}^{-2},$ $96$ $N$

Three blocks each of mass m are hanged vertically with the help of inextensible strings and ideal springs. Initially, the system was in equilibrium. If at any instant, the lowermost string is cut, then the acceleration of block B just after cutting the string will be:

The angle between the position vector and the acceleration vector of a particle in non-uniform circular motion (centre of the circle is taken as the origin) will be:

1. 0°

2. 45°

3. 75°

4. 135°

A particle of mass ‘m’ having speed v goes in a vertical circular motion such that its centre is at its origin, as shown in the figure. If at any instant the angle made by the string with a negative y-axis is $\theta$ then the tension in the string is:
[Take radius = R]

$1.$ $mg\sin \theta +\frac{m{v}^2}{R}$
$2.\hspace{0.17em}mg\cos \theta -\frac{m{v}^2}{R}$
$3.\hspace{0.17em}\hspace{0.17em}mg\cos \theta +\frac{m{v}^2}{R}$
$4.\hspace{0.17em}\hspace{0.17em}mg\sin \theta -\frac{m{v}^2}{R}$