Three blocks of mass $5 \ kg$ each are suspended from a ceiling as shown in the figure. The value of $\frac{T_3}{T_1}$ is .............

If the tension in the cable of a $1000 \,kg$ elevator is $1000 \,kg$ weight,the elevator

Two men of unequal masses hold on to the two sections of a light rope passing over a smooth light pulley. Which of the following are possible?

Objects $A$ and $B$,each of mass $m$,are connected by a light inextensible cord. They are constrained to move on a frictionless ring in a vertical plane as shown in the figure. The objects are released from rest at the positions shown. The tension in the cord just after release will be

$A$ bob of mass $m$ is hanging from a pulley inside a car by a string. The other end of the string is held by a person standing in the car. The car is moving with a constant horizontal acceleration '$a$' as shown in the figure. The other end of the string is pulled with a constant acceleration '$a$' vertically downward. The tension in the string is equal to-

Two bodies of mass $4 \, kg$ and $6 \, kg$ are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is