$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 ~m$ apart. The distance between successive node and antinode is (in $~m$)

Which of the following statements is correct for any thermodynamic system?

$A$ particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

$A$ system is provided with $50 \ J$ of heat and the work done on the system is $10 \ J$. What is the change in internal energy of the system in joules?

Two positively charged particles $m_{1}$ and $m_{2}$ have been accelerated across the same potential difference of $200 \ keV$ as shown below. Given mass of $m_{1} = 1 \ amu$ and $m_{2} = 4 \ amu$. The de Broglie wavelength of $m_{1}$ will be $x$ times that of $m_{2}$. The value of $x$ is . . . . . . . (nearest integer)

$A$ body is executing simple harmonic motion. At a displacement $x$ its potential energy is $E_1$ and at a displacement $y$ its potential energy is $E_2$. The potential energy $(E)$ at displacement $(x+y)$ is