An electric motor of power $100\, W$ is used to drive the stirrer in a water bath. If $50\%$ of the energy supplied to the motor is spent in stirring the water, calculate the work done on the water in one minute. (in $J$)

Calculate the electricity bill amount for the month of April if $4$ bulbs of $40 \, W$ for $5 \, hrs$, $4$ tube lights of $60 \, W$ for $5 \, hrs$, a $TV$ of $100 \, W$ for $6 \, hrs$, and a washing machine of $400 \, W$ for $3 \, hrs$ are used per day. The cost per unit is ₹ $1.80$.

Justify,giving proper reasoning,whether the work done in the following case is positive or negative: Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

State whether the following statement is true or false:
When a body falls on the ground and stops,the principle of conservation of energy is violated.

$A$ $1 \, kg$ mass has a kinetic energy of $1 \, J$ when its speed is: (in $, m/s$)

$(a)$ Define potential energy. Write an expression for potential energy of an object of mass $m$ raised through a height $h$.
$(b)$ Find the energy possessed by an object of mass $10 \, kg$ when it is raised to a height of $6 \, m$ above the ground. (Given $g = 9.8 \, m s^{-2}$)