The energy of the electron in the first orbit of $He^{+}$ is $-871.6 \times 10^{-20} \ J$. The energy of the electron in the first orbit of hydrogen would be

If a unit vector is represented by $0.5\hat{i} - 0.8\hat{j} + c\hat{k}$,then the value of $c$ is:

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$).

If $E, M, J$ and $G$ respectively denote energy,mass,angular momentum,and universal gravitational constant,the quantity which has the same dimensions as the dimensions of $\frac{E J^2}{M^5 G^2}$ is:

Which one of the following is a correct statement?

Two towers $A$ and $B$,each of height $20 \ m$,are situated a distance $200 \ m$ apart. $A$ body is thrown horizontally from the top of tower $A$ with a velocity $20 \ ms^{-1}$ towards tower $B$ and hits the ground at point $P$. Another body is thrown horizontally from the top of tower $B$ with a velocity $30 \ ms^{-1}$ towards tower $A$ and hits the ground at point $Q$. If a car starting from rest from point $P$ reaches point $Q$ in $10 \ s$,the acceleration of the car is . . . . . . . (Acceleration due to gravity $g = 10 \ ms^{-2}$) (in $ms^{-2}$)