When a body is subjected to a direct tensile stress (σ) in one plane, then maximum normal stress occurs at a section inclined at _________ to the normal of the section.

When a body is subjected to a direct tensile stress ($$\sigma $$) in one plane, then normal stress on an oblique section of the body inclined at an angle $$\theta $$ to the normal of the section is

A

$$\sigma \cos \theta $$

B

$$\sigma {\cos ^2}\theta $$

C

$$\sigma \sin\theta $$

D

$$\sigma {\sin ^2}\theta $$

When a body is subjected to a direct tensile stress ($$\sigma $$) in one plane, then tangential or shear stress on an oblique section of the body inclined at an angle $$\theta $$ to the normal of the section is

A

$$\sigma \sin 2\theta $$

B

$$\sigma \cos 2\theta $$

C

$$\frac{\sigma }{2}\sin 2\theta $$

D

$$\frac{\sigma }{2}\cos 2\theta $$

A body is subjected to a direct tensile stress (σ) in one plane. The shear stress is maximum at a section inclined at __________ to the normal of the section.

A

45° and 90°

B

45° and 135°

C

60° and 150°

D

30° and 135°

When a body is subjected to a direct tensile stress (σ) in one plane, the maximum shear stress is __________ the maximum normal stress.

A

Equal to

B

One-half

C

Two-third

D

Twice

When a body is subjected to a direct tensile stress ($${\sigma _{\text{x}}}$$) in one plane accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), the maximum shear stress is

A

$$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{{{\sigma _{\text{x}}}}}{2} - \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

C

$$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 - 4\tau _{{\text{xy}}}^2} $$

D

$$\frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

The velocity ratio in case of an inclined plane inclined at angle 'θ' to the horizontal and weight being pulled up the inclined plane by vertical effort is

A

sinθ

B

cosθ

C

tanθ

D

cosecθ

The change in length due to a tensile or compressive force acting on a body is given by (where P = Tensile or compressive force acting on the body, $$l$$ = Original length of the body, A = Cross-sectional area of the body and E = Young's modulus for the material of the body)

A

$$\frac{{{\text{P}}l{\text{A}}}}{{\text{E}}}$$

B

$$\frac{{{\text{P}}l}}{{{\text{AE}}}}$$

C

$$\frac{{\text{E}}}{{{\text{P}}l{\text{A}}}}$$

D

$$\frac{{{\text{AE}}}}{{{\text{P}}l}}$$

A body of weight 'W' is required to move up on rough inclined plane whose angle of inclination with the horizontal is 'α'. The effort applied parallel to the plane is given by (where μ = tanφ = Coefficient of friction between the plane and the body.)

A

P = W tanα

B

P = W tan (α + φ)

C

P = W (sinα + μcosα)

D

P = W (cosα + μsinα)

When a body is subjected to biaxial stress i.e. direct stresses ($${\sigma _{\text{x}}}$$) and ($${\sigma _{\text{y}}}$$) in two mutually perpendicular planes accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), then maximum shear stress is

A

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

C

$$\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

D

$$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is

A

Zero

B

Maximum

C

Minimum

D

None of these

When a body is subjected to a direct tensile stress (σ) in one plane, then maximum normal stress occurs at a section inclined at _________ to the normal of the section.

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