The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T, so that its new temperature is T $$+$$ ∆T. The increase in the volume of the sphere is approximately, $${NCERT$$ Exemplar]

Question

The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T, so that its new temperature is T $$+$$ ∆T. The increase in the volume of the sphere is approximately, $${NCERT$$ Exemplar]

Infinity Learn · Accepted Answer

Let the radius of the sphere be R. As the temperature increases, radius of the sphere increases as shown in figure.Original volume, Coefficient of linear expansion $$=$$ α∴Coefficient of volume expansion $$=$$ $$3$$α∴  $$1VdVdT=3$$α⇒$$dV=3V$$αdT≈$$4$$$$π$$$$R3$$αΔT                    $$=$$ Increase in the volume

	Column - I		Column - II
a	$γ_{g} < γ_{R}$	p	liquid level rises continuously from beginning
b	$γ_{g} = γ_{R}$	q	liquid level falls continuously from beginning
c	$γ_{g} > γ_{R}$	r	liquid level remains same
d	$γ_{g} = 0$	s	liquid level first falls and then rises

The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is $α$ . The sphere is heated a little by a temperature $∆$ T, so that its new temperature is T + $∆$ T. The increase in the volume of the sphere is approximately, {NCERT Exemplar]

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T, so that its new temperature is T + ∆T. The increase in the volume of the sphere is approximately, {NCERT Exemplar]

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is $α$ . The sphere is heated a little by a temperature $∆$ T, so that its new temperature is T + $∆$ T. The increase in the volume of the sphere is approximately, {NCERT Exemplar]