$A$ bullet moving with a velocity of $100\, m/s$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet,when the velocity is doubled,will be

$A$ ball is thrown from $10 \, m$ height at speed $v_0$ vertically downward. Upon colliding with the surface of the earth,it loses $50 \%$ of its energy and again reaches the same height. The value of $v_0$ is: ................. $m/s$

$A$ target is made of two plates,one of wood and the other of iron. The thickness of the wooden plate is $4\,cm$ and that of the iron plate is $2\,cm$. $A$ bullet fired goes through the wood first and then penetrates $1\,cm$ into the iron. $A$ similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\,cm$ into the wood. If $a_1$ and $a_2$ are the retardations offered to the bullet by the wood and iron plates respectively,then:

Explain the different forms of energy.
$(a)$ Heat Energy
$(b)$ Chemical Energy
$(c)$ Electrical Energy

$A$ body of mass $2 \, \text{kg}$ moving with a speed of $4 \, \text{m/s}$ makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its initial speed. The speed of the two-body centre of mass is $\frac{x}{10} \, \text{m/s}$. Then the value of $x$ is ..... .

$A$ lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it,the initial speed of the bullet is ............ $m \, s^{-1}$.
(Given: Initial temperature of the bullet $= 127^{\circ} C$,
Melting point of the bullet $= 327^{\circ} C$,
Latent heat of fusion of lead $= 2.5 \times 10^{4} \, J \, kg^{-1}$,
Specific heat capacity of lead $= 125 \, J \, kg^{-1} K^{-1}$)