Two bodies moving towards each other collide and move away in opposite directions. There is some rise in temperature of bodies because a part of the kinetic energy is converted into
Heat energy
Electrical energy
Nuclear energy
Mechanical energy
The potential energy of a particle oscillating along $x-$ axis is given as $U = 20 + (x - 2)^2$ where $U$ is in joules and $x$ in $meters$ . Total mechanical energy of the particle is $36\,\, J$ . Maximum kinetic energy of the particle is ................ $\mathrm{J}$
$300$ Joule of work is done in sliding up a $2 \,kg$ block on an inclined plane to a height of $10\, metres$. Taking value of acceleration due to gravity $‘g’ $ to be $10 \,m/s^2$, work done against friction is ........ $J$
Column $II$ gives certain systems undergoing a process. Column $I$ suggests changes in some of the parameters related to the system. Match the statements in Column $I$ to the appropriate process$(es)$ from Column $II$.
Column $I$ | Column $II$ |
$(A)$ The energy of the system is increased |
$(p)$ $System:$ A capacitor, initially uncharged $Process:$ It is connected to a battery |
$(B)$ Mechanical energy is provided to the system, which is converted into energy of random motion of its parts |
$(q)$ $System:$ A gas in an adiabatic container fitted with an adiabatic piston $Process:$ The gas is compressed by pushing the piston |
$(C)$ Internal energy of the system is converted into its mechanical energy |
$(r)$ $System:$ A gas in a rigid container $Process:$ The gas gets cooled due to colder atmosphere surrounding it |
$(D)$ Mass of the system is decreased |
$(s)$ $System:$ A heavy nucleus, initially at rest $Process:$ The nucleus fissions into two fragments of nearly equal masses and some neutrons are emitted |
$(t)$ $System:$ A resistive wire loop $Process:$ The loop is placed in a time varying magnetic field perpendicular to its plane |
A block of mass $m$ is sliding down an inclined plane with constant speed.At a certain instant $t_0$, its height above the ground is $h$. The coefficient of kinetic friction between the block and the plane is $\mu$. If the block reaches the ground at a later instant $t_g$, then the energy dissipated by friction in the time interval $\left(t_g-t_0\right)$ is
On complete combustion a litre of petrol gives off heat equivalent to $3\times 10^7\,J$. In a test drive, a car weighing $1200\,kg$ including the mass of driver, runs $15\,km$ per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were $0.5$.