A particle experiences a variable force $$\overrightarrow F = \left( {4x\widehat i + 3{y^2}\widehat j} \right)$$ in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, then Kinetic Energy changes by :

The approximate height from the surface of earth at which the weight of the body becomes $${1 \over 3}$$ of its weight on the surface of earth is :

[Radius of earth R = 6400 km and $$\sqrt 3 $$ = 1.732]

A resistance of 40 $$\Omega$$ is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :

The equations of two waves are given by :

y₁ = 5 sin 2$$\pi$$(x - vt) cm

y₂ = 3 sin 2$$\pi$$(x $$-$$ vt + 1.5) cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is :