A spring has length ' $L$ ' and force constant ' $K$ '. It is cut into two springs of length ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' such that $\mathrm{L}_1=\mathrm{nL}_2$ ( n is an integer). The force constant of the spring of length ' $\mathrm{L}_2$ ' is
The period of revolution of planet A around the sun is 8 times that of $B$. The distance of $A$ from the sun is how many times greater than that of $B$ from the sun?
In Young's double slit experiment, fringe width is 1.4 mm with light of wavelength $6000 $$\mathop {\rm{A}}\limits^{\rm{o}} $. If the light of wavelength $5400 $$\mathop {\rm{A}}\limits^{\rm{o}} $ is used, with no other change in the experimental set up. The change in fringe width is
Radioactive materials A and B have decay constants ' $9 \lambda$ ' and ' $\lambda$ ' respectively. Initially they have same number of nuclei. The ratio of number of nuclei of material ' $A$ ' to that of ' $B$ ' will be $\left(\frac{1}{\mathrm{e}}\right)$ after time ' $t$ '. So ' $t$ ' is equal to