Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $$d=\frac{R}{2}$$ from the surface of earth, if its weight on the surface of earth is 200 N, will be:

(Given R = radius of earth)

A zener diode of power rating 1.6 W is to be used as voltage regulator. If the zener diode has a breakdown of 8V and it has to regulate voltage fluctuating between 3 V and 10 V. The value of resistance R_s for safe operation of diode will be

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity

A transverse harmonic wave on a string is given by

$$y(x,t) = 5\sin (6t + 0.003x)$$

where x and y are in cm and t in sec. The wave velocity is _______________ ms$$^{-1}$$.