Online Test: Mechanical Properties of Solids | Class 11 Physics

Question 1 of 20

Stress is defined as:

force per unit length

force per unit area

force per unit volume

change in length per unit length

Explanation: Stress $=\frac{F}{A}$, the internal restoring force per unit cross-sectional area.

Question 2 of 20

The SI unit of stress is:

N

N/m

N/m$^2$

no unit

Explanation: Stress is force per unit area, so its unit is $\text{N/m}^2$ (pascal).

Question 3 of 20

Strain is:

measured in pascal

measured in newton

dimensionless

measured in m$^2$

Explanation: Strain is a ratio of like quantities, hence dimensionless with no unit.

Question 4 of 20

Hooke's law holds:

up to the fracture point

only beyond the yield point

within the elastic limit

for gases only

Explanation: Stress is proportional to strain only within the elastic (proportional) limit.

Question 5 of 20

A tangential force applied to a face produces:

tensile stress

compressive stress

shear stress

hydraulic stress

Explanation: A force parallel to a face slides layers over one another, producing shear (tangential) stress.

Question 6 of 20

Young's modulus is given by:

$\frac{A\Delta L}{FL}$

$\frac{FL}{A\Delta L}$

$\frac{F\Delta L}{AL}$

$\frac{FA}{L\Delta L}$

Explanation: $Y=\frac{\text{stress}}{\text{strain}}=\frac{F/A}{\Delta L/L}=\frac{FL}{A\Delta L}$.

Question 7 of 20

The dimensional formula of stress is:

$[\text{MLT}^{-2}]$

$[\text{ML}^{-1}\text{T}^{-2}]$

$[\text{ML}^2\text{T}^{-2}]$

$[\text{M}^0\text{L}^0\text{T}^0]$

Explanation: Stress $=\frac{\text{force}}{\text{area}}=\frac{[\text{MLT}^{-2}]}{[\text{L}^2]}=[\text{ML}^{-1}\text{T}^{-2}]$.

Question 8 of 20

A steel wire of area $1\times10^{-6}\ \text{m}^2$ carries a 50 N load. The tensile stress is:

$5\times10^{6}\ \text{N/m}^2$

$5\times10^{7}\ \text{N/m}^2$

$5\times10^{8}\ \text{N/m}^2$

$50\ \text{N/m}^2$

Explanation: Stress $=\frac{50}{1\times10^{-6}}=5\times10^{7}\ \text{N/m}^2$.

Question 9 of 20

The bulk modulus is defined as:

$-\frac{\Delta P}{\Delta V/V}$

$\frac{\Delta V/V}{\Delta P}$

$\frac{F/A}{\theta}$

$\frac{FL}{A\Delta L}$

Explanation: $B=-\frac{\Delta P}{\Delta V/V}$; the negative sign keeps $B$ positive as volume decreases under pressure.

Question 10 of 20

Compressibility is:

the square of bulk modulus

the reciprocal of bulk modulus

equal to Young's modulus

always zero for liquids

Explanation: Compressibility $k=\frac{1}{B}$.

Question 11 of 20

The shear (rigidity) modulus is possessed by:

gases only

liquids only

solids only

all states of matter equally

Explanation: Only solids resist a change of shape; fluids at rest cannot sustain shear stress.

Question 12 of 20

Poisson's ratio is the ratio of:

longitudinal stress to strain

lateral strain to longitudinal strain

shear stress to shear strain

volume strain to pressure

Explanation: $\sigma=-\frac{\text{lateral strain}}{\text{longitudinal strain}}$, a dimensionless number.

Question 13 of 20

For most metals Poisson's ratio lies roughly between:

$0$ and $0.1$

$0.2$ and $0.4$

$0.6$ and $0.8$

$1$ and $2$

Explanation: Typical metals have $\sigma\approx0.2$–$0.4$.

Question 14 of 20

The elastic potential energy stored in a stretched wire is:

$F\Delta L$

$\frac{1}{2}F\Delta L$

$2F\Delta L$

$\frac{F}{\Delta L}$

Explanation: Average force is $\frac{F}{2}$, so $U=\frac{1}{2}F\Delta L$.

Question 15 of 20

The elastic energy stored per unit volume equals:

$\text{stress}\times\text{strain}$

$\frac{1}{2}\times\text{stress}\times\text{strain}$

$\frac{\text{strain}}{\text{stress}}$

$\frac{1}{2}\times\frac{\text{strain}}{\text{stress}}$

Explanation: Energy density $u=\frac{1}{2}\times\text{stress}\times\text{strain}$.

Question 16 of 20

On the stress–strain curve, the point beyond which a body does not regain its original shape is the:

proportional limit

elastic limit

origin

ultimate strength

Explanation: Beyond the elastic limit the deformation becomes permanent (plastic).

Question 17 of 20

The gradual loss of strength of a material under repeated stress cycles is called:

elastic after-effect

elastic fatigue

ductility

yielding

Explanation: Elastic fatigue is the weakening that occurs after many loading–unloading cycles.

Question 18 of 20

A wire stretches by 2 mm under a force of 200 N. The elastic energy stored is:

$0.2\ \text{J}$

$0.4\ \text{J}$

$0.8\ \text{J}$

$4\ \text{J}$

Explanation: $U=\frac{1}{2}\times200\times2\times10^{-3}=0.2\ \text{J}$.

Question 19 of 20

Among steel, copper and rubber, the material with the largest Young's modulus is:

rubber

copper

steel

all equal

Explanation: Steel ($Y\approx2\times10^{11}\ \text{N/m}^2$) is the stiffest of the three.

Question 20 of 20

Bridge girders are given an I-section mainly to:

increase weight

reduce stiffness

give high stiffness with minimum material

lower the Young's modulus

Explanation: An I-section concentrates material where bending stress is greatest, giving strength with low weight.

Online Test — Mechanical Properties of Solids