A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $${1 \over 4}$$ times that of the bob and the length of the thread is increased by 1/3^rd of the original length, then the time period of the simple harmonic oscillations will be :-

Statement : 1

If three forces $${\overrightarrow F _1},{\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ are represented by three sides of a triangle and $${\overrightarrow F _1} + {\overrightarrow F _2} = - {\overrightarrow F _3}$$, then these three forces are concurrent forces and satisfy the condition for equilibrium.

Statement : 2

A triangle made up of three forces $${\overrightarrow F _1}$$, $${\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.

In the light of the above statements, choose the most appropriate answer from the options given below :

If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :

The magnetic field vector of an electromagnetic wave is given by $$B = {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos (kz - \omega t)$$; where $$\widehat i,\widehat j$$ represents unit vector along x and y-axis respectively. At t = 0s, two electric charges q₁ of 4$$\pi$$ coulomb and q₂ of 2$$\pi$$ coulomb located at $$\left( {0,0,{\pi \over k}} \right)$$ and $$\left( {0,0,{{3\pi } \over k}} \right)$$, respectively, have the same velocity of 0.5 c $$\widehat i$$, (where c is the velocity of light). The ratio of the force acting on charge q₁ to q₂ is :-