Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
$4$
$3$
$2$
$1$
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 After the force is withdrawn block $A$ executes small oscillations.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
The dimensions of physical quantity $X$ in the equation Force $ = \frac{X}{{{\rm{Density}}}}$ is given by
If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G,\,c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?
$(1)$ The dimension of force is $L ^{-3}$
$(2)$ The dimension of energy is $L ^{-2}$
$(3)$ The dimension of power is $L ^{-5}$
$(4)$ The dimension of linear momentum is $L ^{-1}$
In a particular system of units, a physical quantity can be expressed in terms of the electric charge $c$, electron mass $m_c$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_0}$, where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B]=[c]^\alpha\left[m_c\right]^\beta[h]^\gamma[k]^\delta$. The value of $\alpha+\beta+\gamma+\delta$ is. . . . .