A rope of length $5\,m$ is kept on frictionless surface and a force of $5\,N$ is applied to one of its end. Find tension in the rope at $1\,m $ from this end ......... $N$

A balloon of mass $M$ is descending at a constant acceleration $\alpha $. When a mass $m$ is released from the balloon it starts rising with the same acceleration $\alpha $. Assuming that its volume does not change, what is the value of $m$ ?

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface., the acceleration of mass $m$ is

A rod of length $L$ and mass $M$ is acted on by two unequal forces $F_1$ and $F_2 (< F_1 )$ as shown in the following figure.The tension in the rod at a distance $y$ from the end $A$ is given by

Three blocks of masses $2 \,kg, 3 \,kg$ and $5\, kg$ are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force $F = 10N,$ then tension ${T_1} = $  .......... $N$ 

Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. $A$ vertical force $\overrightarrow{ P }$ of magnitude $100 \;N$ is applied at point $A$ of the frame. Suppose the force is $\overrightarrow{ P }$ resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ............

[Given : $\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819$ $\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]$