JEE Advanced (Fill in the Blanks): Mechanical Properties of Solids & Fluids | Chapter-wise Tests for JEE Main & Advanced PDF Download

Fill in the Blanks

Q.1. A wire of length L and cross sectional area A is made of a material of Young’s modulus Y. If the wire is stretched by an amount x, the work done is ................. (1987 - 2 Marks)

Ans. 

Solution.

 Q.2. A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless pistion of area A floats on the surface of the liquid.

When a mass M  is placed on the piston to compress the liquid the fractional change in the radius of the sphere, δ R/R, is ...........     (1988 - 2 Mark)

Ans. Mg/3Ak

Solution. 

Q.3. A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are λ₁ and λ₂ respectively. If the temperatures of both mercury and the metal are increased by an amount ΔT , the fraction of the volume of the metal submerged in mercury changes by the factor ...................       (1991 - 2 Mark)

Ans. (λ₂ - λ₁)ΔT

Solution. KEY CONCEPT

Using the relation for floatation, vd_Hgg = Vd_mg 

Fraction of volume of metal submerged in mercury

In second case, when temperature is increased by ΔT.

= Fraction of volume of metal submerged in mercury = K₂ (say)

i.e., metal block will get immersed deeper 

If λ₂ < λ₁ then k₂ < k₁ 

i.e. metal block will rise a bit as compared to its previous position.

Q.4. A horizontal pipeline carries water in a streamline flow.

At a point along the pipe, where the cross- sectional area is 10 cm², the water velocity is 1 ms^–1 and  the pressure is 2000 Pa. The pressure of water at another point where the cross-sectional area is 5 cm², is... Pa. 

(Density of water = 10³ kg.m^–3)               (1994 - 2 Marks)

Ans. 500 Pa.

Solution. KEY CONCEPT

Applying equation of continuity at cross section 1 and 2

A₁v₁ = A₂v₂ ⇒  10 × 1 = 5 × v₂ ⇒ v₂ = 2m/s

Applying Bernoulli's theorem