$A$ ball of mass $m_1$ and another ball of mass $m_2$ are dropped from the same height. If the time taken by the balls to reach the ground is $t_1$ and $t_2$ respectively,then:

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

Half-life of a radioactive substance $A$ is two times the half-life of another radioactive substance $B$. Initially,the number of nuclei of $A$ and $B$ are $N_A$ and $N_B$ respectively. After three half-lives of $A$,the number of nuclei of both are equal. Then the ratio $\frac{N_A}{N_B}$ is

$A$ solid sphere and a disc of same mass $M$ and radius $R$ are kept such that their curved surfaces are in contact and their centers lie along the same horizontal line. The moment of inertia of the two-body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

The $pK_a$ values of four carboxylic acids are given below. Identify the weakest carboxylic acid.

Magnesium wire is heated in the atmosphere of $CO_2$ because