A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly onto another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta $ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn block $A$ executes small oscillations. The time period of which is given by
$2\pi \sqrt {\frac{{M\eta }}{L}} $
$2\pi \sqrt {\frac{L}{{M\eta }}} $
$2\pi \sqrt {\frac{{ML}}{\eta }} $
$2\pi \sqrt {\frac{M}{{\eta L}}} $
If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are
What is dimensional analysis ? Write limitation of dimensional analysis.
The position of a particle at time $t$ is given by the relation $x(t) = \left( {\frac{{{v_0}}}{\alpha }} \right)\,\,(1 - {e^{ - \alpha t}})$, where ${v_0}$ is a constant and $\alpha > 0$. The dimensions of ${v_0}$ and $\alpha $ are respectively
If $x$ and $a$ stand for distance then for what value of $n$ is given equation dimensionally correct the eq. is $\int {\frac{{dx}}{{\sqrt {{a^2}\, - \,{x^n}} \,}}\, = \,{{\sin }^{ - 1}}\,\frac{x}{a}} $