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$1$ joule of energy is to be converted into new system of units in which length is measured in $10$ metre, mass in $10 \,kg$ and time in $1$ minute. The numerical value of $1 \,J$ in the new system is
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 After the force is withdrawn block $A$ executes small oscillations.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
Even if a physical quantity depends upon three quantities, out of which two are dimensionally same, then the formula cannot be derived by the method of dimensions. This statement