Answer

Verified

33.6k+ views

**Hint**When a body is deformed by an external force, the internal restoring forces will oppose this force and restore the original shape of the object. This restoring force developed per unit area is called stress. The ratio of change in dimension to the original dimension is called strain.

**Complete Step by step solution**

According to Hooke’s law within the elastic limit, stress is proportional to strain

Stress $ \propto $strain

$ \Rightarrow \dfrac{{stress}}{{strain}} = const$

This constant is called the modulus of elasticity.

Stress can be defined as the force per unit area, i.e.

Stress = $\dfrac{F}{a}$

We know that force, $F = ma$

The dimensional formula for force is $F = m \times a = \left[ {ML{T^{ - 2}}} \right]$

The area is given by length $ \times $breadth

The dimensional formula for the area can be written as, $a = l \times b = \left[ {{M^0}{L^2}{T^0}} \right]$

The dimensional formula for stress can be written as,

Stress $ = \dfrac{{\left[ {ML{T^{ - 2}}} \right]}}{{\left[ {{M^0}{L^2}{T^0}} \right]}}$

The dimensional formula for linear stress can be written as,

Stress $ = \left[ {M{L^{ - 1}}{T^{ - 2}}} \right]$

The strain is a dimensionless quantity.

Therefore, the dimensional formula for modulus of elasticity can be written as,

Modulus of elasticity $ = \dfrac{{\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]}}{{\left[ {{M^0}{L^0}{T^0}} \right]}} = \left[ {M{L^{ - 1}}{T^{ - 2}}} \right]$

**The answer is: Option (A): $\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]$**

**Additional information**

An equation connecting the physical quantity with its dimensional formula is called the dimensional equation of that physical quantity. The dimensions of the same fundamental quantity must be the same on either side of a dimensional equation.

**Note**

All physical quantities can be expressed as a combination of seven fundamental or base quantities. The dimensional formula of a given physical quantity is an expression showing the dimensions of the fundamental quantities. Dimensions of a physical quantity are the powers to which the base quantities are to be raised to represent that quantity.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Other Pages

The force of interaction of two dipoles if the two class 12 physics JEE_Main

Dissolving 120g of urea molwt60 in 1000g of water gave class 11 chemistry JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

Oxidation state of S in H2S2O8 is A 6 B 7 C +8 D 0 class 12 chemistry JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main