The volume of one mole of the gas is changed from $V$ to $2 V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas,what is the change in internal energy of the gas?

Which of the following pairs of an animal and a plant represents endangered organisms in India?

The plates of a parallel plate capacitor are charged up to $200 \ V$. $A$ dielectric slab of thickness $4 \ mm$ is inserted between its plates. Then,to maintain the same potential difference between the plates of the capacitor,the distance between the plates is increased by $3.2 \ mm$. The dielectric constant of the dielectric slab is:

If $P_1, P_2, P_3$ are the perimeters of the three circles $x^2+y^2+8x-6y=0$,$4x^2+4y^2-4x-12y-186=0$,and $x^2+y^2-6x+6y-9=0$ respectively,then

$1\, kg$ of a diatomic gas is at a pressure of $8 \times 10^4\, N/m^2$. The density of the gas is $4\, kg/m^3$. What is the energy of the gas due to its thermal motion?

$A$ nucleus at rest undergoes $\alpha-$ decay according to the equation ${}_{92}^{226}X \to Y + \alpha$. At $t = 0$,the emitted $\alpha-$ particle enters a region of space where a uniform magnetic field $\vec{B} = B_0 \hat{i}$ and an electric field $\vec{E} = E_0 \hat{i}$ exist. The $\alpha-$ particle enters the region with velocity $\vec{v} = v_0 \hat{j}$ at $x = 0$. After a time $t = \sqrt{3} \times 10^7 \frac{m_{\alpha}}{q_{\alpha} E_0}$,the particle is found to have twice its initial speed. What is the initial speed $v_0$ of the $\alpha-$ particle?