A semicircular disc rests on a horizontal surface with its top flat surface horizontal and circular portion touching down. The coefficient of friction between semi circular disc and horizontal surface is µ. This disc is to be pulled by a horizontal force applied at one edge and it always remains horizontal. When the disc is about to start moving, its top horizontal force will

For a shoe brake, the equivalent coefficient of friction is equal to (where $$\mu $$ = Actual coefficient of friction and $$\theta $$ = Semi-block angle)

A

$$\frac{{2\mu \sin \theta }}{{\theta + \sin \theta }}$$

B

$$\frac{{\mu \sin \theta }}{{2\theta + \sin 2\theta }}$$

C

$$\frac{{4\mu \sin \theta }}{{\theta + \sin \theta }}$$

D

$$\frac{{4\mu \sin \theta }}{{2\theta + \sin 2\theta }}$$

A box of weight 500 N is being pulled over the floor with a horizontal force of 150N. What is the coefficient of friction between the floor and the box?

A

0.1

B

0.2

C

0.3

D

0.4

A box of weight 500 N is being pulled over the floor with a horizontal force of 150 N. what is the coefficient of between the floor and the box?

A

0.1

B

0.2

C

0.3

D

`0.4

A plate with an elliptical hole in the centre, with semi-major axis (a) perpendicular to the direction of loading and semi-minor axis (b) along the direction of loading, is subjected to a pull P. The maximum stress induced at the edge of the hole is equal to (where $$\sigma $$ = Stress for a plate with no hole i.e. nominal stress)

A

$$\sigma \left( {1 + \frac{{\text{b}}}{{2{\text{a}}}}} \right)$$

B

$$\sigma \left( {1 + \frac{{2{\text{a}}}}{{\text{b}}}} \right)$$

C

$$\sigma \left( {1 + \frac{{\text{b}}}{{3{\text{a}}}}} \right)$$

D

$$\sigma \left( {1 + \frac{{3{\text{a}}}}{{\text{b}}}} \right)$$

A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$ = Angular velocity of precession of the axis of spin)

A

$$\frac{1}{2}I{\omega ^2}$$

B

$$I{\omega ^2}$$

C

$$\frac{1}{2}I\omega \omega {\text{P}}$$

D

$$I\omega \omega {\text{P}}$$

The horizontal thrust on the ends of a two hinged semicircular arch of radius ‘R’ carrying

A

A uniformly distributed load $$\omega $$ per unit run over its right half span, is $$\frac{2}{3}\frac{{\omega {\text{R}}}}{\pi }$$

B

A uniformly distributed load $$\omega $$ per unit run over its entire span is $$\frac{4}{3}\frac{{\omega {\text{R}}}}{\pi }$$

C

A distributed load varying from zero at the left end to $$\omega $$ per unit horizontal run at the right end, is $$\frac{2}{3}\frac{{\omega {\text{R}}}}{\pi }$$

D

All the above

In a band and block brake, the ratio of tensions on tight side and slack side of the band is (where $$\mu $$ = Coefficient of friction between the blocks and the drum, $$\theta $$ = Semi-angle of each block subtending at the center of drum and n = Number of blocks)

A

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}} = \mu \theta {\text{n}}$$

B

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}} = {\left( {\frac{{1 - \mu \tan \theta }}{{1 + \mu \tan \theta }}} \right)^{\text{n}}}$$

C

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}} = {\left( {\mu \theta } \right)^{\text{n}}}$$

D

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}} = {\left( {\frac{{1 + \mu \tan \theta }}{{1 - \mu \tan \theta }}} \right)^{\text{n}}}$$

In a band and block brake, the ratio of tensions on the tight and slack sides of band is given by (where $$\mu $$ = Coefficient of friction between the blocks and the drum, $$\theta $$ = Semi-angle of each block subtending at the centre of drum and n = Number of blocks)

A

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_{\text{2}}}}} = \mu \theta \times {\text{n}}$$

B

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}} = {\left( {\mu \theta } \right)^{\text{n}}}$$

C

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}} = {\left( {\frac{{1 - \mu \tan \theta }}{{1 + \mu \tan \theta }}} \right)^{\text{n}}}$$

D

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}} = {\left( {\frac{{1 + \mu \tan \theta }}{{1 - \mu \tan \theta }}} \right)^{\text{n}}}$$

The frictional torque transmitted in a flat pivot bearing, considering uniform wear, is (where μ = Coefficient of friction, W = Load over the bearing and R = Radius of bearing surface)

A

$$\frac{1}{2}$$μWR

B

$$\frac{2}{3}$$μWR

C

$$\frac{3}{4}$$μWR

D

μWR

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)

Related Questions