For the given system,find the tension $T_2$ in the upper string.

An electric lift with a maximum load of $2000\,kg$ (lift + passengers) is moving up with a constant speed of $1.5\,m/s$. The frictional force opposing the motion is $3000\,N$. The minimum power delivered by the motor to the lift in watts is: $(g=10\,m/s^2)$

An ideal spring is connected between two blocks of masses $M$ and $m$. This system can move on a smooth horizontal table. The blocks are brought closer to compress the spring and then released. In the subsequent motion,select the true statement$(s)$:
$(a)$ They move in opposite directions with speeds inversely proportional to their masses.
$(b)$ The ratio of their speeds remains constant.
$(c)$ Linear momentum and energy of the system remain conserved.

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth,while the lower half is rough. $A$ block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by:

$A$ motor car moving with velocity $7 \ m/s$ stops in $10 \ m$ distance when brakes are applied. What is the relation between the resistance force $(R)$ and the weight $(W)$ of the car? (Take value of $g = 9.8 \ m/s^2$)

$A$ car of mass $500\, kg$ is driven with acceleration $1\, m/s^2$ along a straight level road against a constant external resistance of $1000\, N$. When the velocity is $5\, m/s$,the rate at which the engine is working is .............. $kW$.