The engine of a jet aircraft applies a thrust force of $10^5 \ N$ during take-off and causes the plane to attain a velocity of $1 \ km/s$ in $10 \ s$. The mass of the plane is:

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

If $x = \sin t$ and $y = \sin pt$,then the value of $(1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} + p^2y$ is equal to

The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0$ for $x>0$ is equal to:

Which of the following statements is incorrect?

$A$ wire of length $l$ is bent into a circular coil of one turn of radius $R_1$. Another wire of the same material,same area of cross-section,and same length is bent into a circular coil of two turns of radius $R_2$. When the same current flows through the two coils,the ratio of magnetic induction at the centres of the two coils is