$A$ metal rod is used as a pendulum. If the room temperature increases by $10^{\circ}C$ and the linear expansion coefficient of the metal is $2 \times 10^{-6} {\circ}C^{-1}$,then the percentage change in the time period of the pendulum is ...... $\%$

$A$ metal block is made from a mixture of $2.4 \ kg$ of aluminium,$1.6 \ kg$ of brass,and $0.8 \ kg$ of copper. The metal block is initially at $20^{\circ} C$. If the heat supplied to the metal block is $44.4 \ cal$,find the final temperature of the block if the specific heats of aluminium,brass,and copper are $0.216, 0.0917, 0.0931 \ cal \cdot kg^{-1} \cdot ^{\circ}C^{-1}$ respectively. (in $^{\circ} C$)

The temperature of a body is given by $T = 6t^2 + 4$. The rate of change of temperature with respect to time at $t = 10 \ s$ is ........ $K/s$. ($T$ is in $Kelvin$ and $t$ is in $seconds$)

The pressure and volume of saturated water vapour are $P$ and $V$ respectively. It is compressed isothermally such that the volume becomes $V/2$. The final pressure will be

$A$ $20 \,g$ bullet whose specific heat is $5000 \,J/(kg \cdot ^{\circ}C)$ and moving at $2000 \,m/s$ plunges into a $1.0 \,kg$ block of wax whose specific heat is $3000 \,J/(kg \cdot ^{\circ}C)$. Both the bullet and the wax are at $25^{\circ}C$. Assuming that $(i)$ the bullet comes to rest in the wax and $(ii)$ all its kinetic energy is converted into heat,the final temperature of the wax (in $^{\circ}C$) is close to:

If in the winter season the surface temperature of a lake is $1^{\circ} C$,the temperature at the bottom of the lake will be ............