`m_1 ` & `m_2` are connected with a light inextensible string with `m_1` lying on smooth table and `m_2` hanging as shown in figure. `m_1` is also connected to a light spring which is initially unstretched an the system is released from rest.

Consider the case of two bodies of masses m_(1) and m_(2) which are connected by light inextensible string passing over a light smooth pulley as shown in the figure. The expression for acceleration of the system and tension of the string are expressed below under different situations: (i) when m_(1) gt m_(2) . In this case a=((m_(1)-m_(2))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g (ii) when m_(2) gt m_(1) . In this case a=((m_(2)-m_(1))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g (iii) When m_(1)=m_(2)=m . In this case a = 0, T = mg What is the tension in the string?

Two blocks of mass m_(1) and m_(2) (m_(1) lt m_(2)) are connected with an ideal spring on a smooth horizontal surface as shown in figure. At t = 0 m_(1) is at rest and m_(2) is given a velocity v towards right. At this moment, spring is in its natural length. Then choose the correct alternative :

Two blocks of mass m_(1) and m_(2) (m_(1) lt m_(2)) are connected with an ideal spring on a smooth horizontal surface as shown in figure. At t = 0 m_(1) is at rest and m_(2) is given a velocity v towards right. At this moment, spring is in its natural length. Then choose the correct alternative :

Two blocks of mass m_(1) and m_(2) (m_(1) lt m_(2)) are connected with an ideal spring on a smooth horizontal surface as shown in figure. At t = 0 m_(1) is at rest and m_(2) is given a velocity v towards right. At this moment, spring is in its natural length. Then choose the correct alternative :

Two masses m_1 = 1 kg and m_2 = 2 kg are connected by a light inextensible string and suspended by means of a weightness pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in two seconds is (Take g = 10 ms^-2 . .

Two masses m_1 = 1 kg and m_2 = 2 kg are connected by a light inextensible string and suspended by means of a weightness pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in two seconds is (Take g = 10 ms^-2 . .

A block of mass m_(1)=2 kg is kept on a smooth horizontal table. Another block of mass m_(2)=1 kg is connected to m_(1) by a light inextensible string passing over a smooth pulley as shown in the figure. If the blocks are released, what will be the (a) acceleration of each block (b) tension in the string?

A block of mass m_(1)=2 kg is kept on a smooth horizontal table. Another block of mass m_(2)=1 kg is connected to m_(1) by a light inextensible string passing over a smooth pulley as shown in the figure. If the blocks are released, what will be the (a) acceleration of each block (b) tension in the string?

Two blocks of masses m and M connected by a light spring of stiffness k, are kept on a smooth horizontal surface as shown in figure. What should be the initial compression of the spring so that the system will be about to break off the surface, after releasing the block m_1 ?