A ladder of weight 'w' rests against a smooth vertical wall and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being $$\frac{1}{4}$$. The maximum angle of inclination of the ladder to the vertical, if a man of weight 'w' is to walk to the top of it safely, is tan<sup>-1</sup>x, where x is

A semi-circular disc rests on a horizontal surface with its top flat surface horizontal and circular portion touching down. The coefficient of friction between semi-cricular disc and horizontal surface is i. 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

A

remain horizontal

B

slant up towards direction of pull

C

slant down towards direction of pull

D

unpredictable

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

A

Remain horizontal

B

Slant up towards direction of pull

C

Slant down towards direction of pull

D

None of the above

If a ladder weighing 250N is placed against a smooth vertical wall having a coefficient of friction between it and floor 0.3, then what is the maximum force of friction available at the point of contact between the ladder and the floor?

A

75N

B

35N

C

50N

D

25N

A leader rests against a wall is perpendicular to the ground if the bottom of the ladder is 4m away from the bottom of the wall, while the top of the ladder is at a height of 3m. What is the length of the ladder.

A

7m

B

35m

C

5m

D

25m

A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous center of rotation when the ladder starts slipping ?
i. 1.0 in from the wall
ii. 1.732 m from the wall
iii. 1.0 m above the floor
iv. 1.732 m above the floor
The correct answer is

A

(i) and (iii)

B

(i) and (iv)

C

(ii) and (iii)

D

(ii) and (iv)

A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being $$\frac{1}{3}$$. The ball rebounds at the same angle. The fraction of its kinetic energy lost is

A

$$\frac{1}{3}$$

B

$$\frac{2}{3}$$

C

$$\frac{1}{9}$$

D

$$\frac{8}{9}$$

A ladder is resting on a rough ground and leaning against a smooth vertical wall. The force of friction will act

A

Downward at its upper end

B

Upward at its upper end

C

Zero at its upper end

D

Perpendicular to the wall at its upper end

A ladder is resting on a smooth ground and leaning against a rough vertical wall. The force of friction will act

A

Towards the wall at its upper end

B

Away from the wall at its upper end

C

Downward at its upper end

D

Upward at its upper end

On a ladder resting on a rough ground and leaning against a smooth vertical wall, the force of friction acts

A

Downwards at its upper end

B

Upwards at its upper end

C