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$$^{-1}$$.

10 resistors each of resistance 10 $$\Omega$$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ___________.

A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5$$\Omega$$, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m/s will be ____________ 10$$^{-3}$$ N.