AIPMT 2009 Preliminary Mock Test

A body of mass $1\text{kg}$ is thrown upwards with a velocity $20\text{m/s}$. It momentarily comes to rest after attaining a height of $18\text{m}$. How much energy is lost due to air friction? ($g=10{\text{m/s}}^2$)

A conducting circular loop is placed in a uniform magnetic field $0.04\text{T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2\text{mm/s}$. The induced emf in the loop when the radius is $2\text{cm}$ is:

The magnetic force acting on a charged particle of charge $-2\mu \text{C}$ in a magnetic field of $2\text{T}$ acting in $y$ direction, when the particle velocity is $(2\hat{i}+3\hat{j})\times 10^6{\text{ms}}^{-1}$, is:

Two bodies of mass $1\text{kg}$ and $3\text{kg}$ have position vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The centre of mass of this system has a position vector:

The electric potential at a point $(x,y,z)$ is given by $V=-x^{2}y-x{z}^3+4$. The electric field $\vec{E}$ at that point is: