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

$\left(\mathrm{a}\right)<mspace\; width="1em"></mspace>2\mathrm{T}<mspace\; width="1em"></mspace>{\mathrm{cos\theta }}_0$
$\left(\mathrm{b}\right)<mspace\; width="1em"></mspace>\mathrm{T}<mspace\; width="1em"></mspace>{\mathrm{cos\theta }}_0$
$\left(\mathrm{c}\right)<mspace\; width="1em"></mspace>2\mathrm{T}<mspace\; width="1em"></mspace>{\mathrm{sin\theta }}_0$
$\left(\mathrm{d}\right)<mspace\; width="1em"></mspace>\mathrm{T}<mspace\; width="1em"></mspace>{\mathrm{sin\theta }}_0$

A massless, frictionless rope is attached at point \(A\) on the wall, then passes under a movable pulley \(P_2,\) goes up and over a fixed ceiling pulley \(P_1,\) and supports a hanging weight \(W_1.\) The movable pulley \(P_2\) carries a second weight \(W_2\)​ hanging directly beneath it. If \(W_1=W_2,\) what is the angle \((AP_2P_1)\) between the two rope segments meeting at \(P_2\text{?}\)
              
1. \(30^\circ\)
2. \(60^\circ\)
3. \(150^\circ\)
4. \(120^\circ\)

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