In the presence of which of the following is the work-energy theorem valid?

$A$ balloon filled with helium rises against gravity,increasing its potential energy. The speed of the balloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy? You can neglect viscous drag of air and assume that the density of air is constant.

What would be the stopping distance if the velocity of a vehicle becomes three times (in $d$)?

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A):$ Kinetic energy of a system can increase without applying external force on the system.
Reason $(R):$ If external forces are absent,then the work done by internal forces is equal to the change in kinetic energy.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ small block slides down from rest at point $A$ on the surface of a smooth cylinder,as shown. At point $B$,the block falls off (leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by

$A$ lorry and a car moving with the same kinetic energy $(K.E.)$ are brought to rest by applying the same retarding force. Then: