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 is (given g = 10 ms^–2) 

(1) 100 ms^–2

(2) 3 ms^–2

(3) 10 ms^–2

(4) 30 ms^–2

Using constraint equations relation between $a_1$ and $a_2$ will be 

1. $a_1$ =3$a_2$

2. a$a_2$ =3$a_1$

3. a$a_2$= 6$a_1$

4. a$a_2$= 7$a_1$

A string with constant tension T is deflected through an angle $2{\theta }_0$ by a smooth fixed pulley. The force on the pulley is

$\left(\mathrm{a}\right) 2\mathrm{T} {\mathrm{cos\theta }}_0$
$\left(\mathrm{b}\right) \mathrm{T} {\mathrm{cos\theta }}_0$
$\left(\mathrm{c}\right) 2\mathrm{T} {\mathrm{sin\theta }}_0$
$\left(\mathrm{d}\right) \mathrm{T} {\mathrm{sin\theta }}_0$

In the figure pulley ${\mathrm{P}}_1$ is fixed and the pulley ${\mathrm{P}}_2$ is movable. If ${\mathrm{w}}_1={\mathrm{w}}_2$, what is the angle between ${\mathrm{AP}}_2{\mathrm{P}}_1$? (pulleys are frictionless)

         
1. 30°

2. 60°

3. 150°

4. 120°

Two blocks of masses \(2\) kg and \(3\) kg are tied at the ends of a light inextensible string passing over a frictionless pulley as shown.

If the system is accelerating upward with acceleration \(5\) m/s², the tension in the string is:
1. \(24\) N
2. \(36\) N
3. \(48\) N
4. \(18\)N