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In Physics, force is defined as: The push or pull on an object with mass that causes it to change its velocity. The Force can be measured using a spring balance. The SI unit of force is Newton(N).
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- Robert Hooke was the scientist who gave Hooke’s law.
- Hooke’s law states that within the elastic limit, stress developed is directly proportional to the strain produced in a body.
- Consider a scenario where we apply external force to the body. As a result stress develops in the body due to this stress there will be a strain produced in the body which implies that there will be some deformation in the body.
- Because of stress, strain is produced.
- According to Hooke’s law, if strain increases the stress will increase and vice-versa.
- The Hooke’s law is applicable to all elastic substances.
- It does not apply to plastic deformation.
- Mathematically :
- stress ∝ strain
- stress = k × strain
- Where k is the proportionality constant and is known as modulus of elasticity.
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Yes, Torque is a example of vector quantity.
Explanation:
Torque is calculated by multiplying force and distance. It is a vector quantity, meaning it has both a direction and a magnitude. Either the angular velocity for the moment of inertia of an object is changing, or both.
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Let the period of oscillation T of a large fluid star depends on the radius of star, R, the mean density of fluid, {tex}\rho{/tex} and universal gravitational constant, G as:
T = k Ra {tex}\rho{/tex}b Gc, where k is a dimensionless constant and a, b, c are their exponents.
Now, equating the dimensions on both the sides, we have,
[Mo Lo T1] = [L]a [M L-3]b [M-1 L3 T-2]c = Mb-c La-3b+3c T-2c
On comparing powers of M, L and T on both sides, we get,
b - c = 0 ...(i)
a - 3b + 3c = 0 ...(ii)
and - 2c = 1 ...(iii)
On simplifying these equations, we get c = {tex}-\frac{1}{2}{/tex}, b = {tex}-\frac{1}{2}{/tex} and a = 0
Thus, period of oscillation, T = {tex}k \rho^{-\frac{1}{2}} G^{-\frac{1}{2}}{/tex}= {tex}\frac{k}{\sqrt{\rho G}}{/tex}
This is the required expression.
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Shubham Kumar 6 years, 2 months ago
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