In an $LCR$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to:

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium,the value of $q$ is

Which of the following is known as 'Oxone'?

The time period of a particle in simple harmonic motion is $8 \ s$. At $t=0$,it is at the mean position. The ratio of the distances travelled by it in the first and second seconds is

The Phthalein test is a characteristic test for which of the following?

$A$ solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. $A$ massless piston of area $a$ floats on the surface of the liquid,covering the entire cross-section of the cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid,the fractional decrement in the radius of the sphere $\left( \frac{dr}{r} \right)$ is