A car of mass $1000\,kg$ negotiates a banked curve of radius $90\,m$ on a fictionless road. If the banking angle is $45^o$, the speed of the car is ......... $ms^{-1}$

An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true

What is the behaviour of perpendicular electric field ${\rm{\vec E}}$ and magnetic field ${\rm{\vec B}}$ ?

A particle having charge of $1 \,\,C$, mass $1 \,\,kg$ and speed $1 \,\,m/s$ enters a uniform magnetic field, having magnetic induction of $1$ $T,$ at an angle $\theta = 30^o$ between velocity vector and magnetic induction. The pitch of its helical path is (in meters) 

A charged particle of charge $q$ and mass $m$, gets deflected through an angle $\theta$ upon passing through a square region of side $a$, which contains a uniform magnetic field $B$ normal to its plane. Assuming that the particle entered the square at right angles to one side, what is the speed of the particle?

A charged particle moves in a magnetic field $\vec B = 10\,\hat i$ with initial velocity $\vec u = 5\hat i + 4\hat j$ The path of the  particle will be