# Friction

## Trending Questions

**Q.**A uniform thin rod of mass M and length L is hinged by a frictionless pivot at its end O, as shown in the diagram. A bullet of mass m moving horizontally with a velocity v, strikes the free end of the rod and gets embedded in it. The angular velocity of the system about O, just after the collision is,

- mvL(M+m)
- 2mvL(M+2m)
- 3mvL(M+3m)
- mvLM

**Q.**A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is

- a=gcosec θ
- a=gsin θ
- a= g cos θ
- a= g tan θ

**Q.**The velocity profile of a fluid over a flat plate is parabolic in nature. At a distance of 15 cm from the plate, the velocity of fluid is maximum i.e 100 cm/s. Calculate the shear stress at a distance of 10 cm from the plate if the viscosity of the fluid is 10 poise.

- 4.53 N/m2
- 2.26 N/m2
- 2.35 N/m2
- None of these

**Q.**

Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel(s = relative density of mercury and ρ = density of water) by

**Q.**A uniform rod of mass m and length L can rotate freely on a smooth horizontal plane about a vertical axis hinged at point O. A point mass having same mass m coming with an initial speed u perpendicular to the rod, strikes the rod in-elastically at its free end. Find out the angular velocity of the rod just after collision?

- ω=4u3L
- ω=3u4L
- ω=5u4L
- ω=4u5L

**Q.**As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m, when released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be :

r√34gh

r√32gh

1r√2gh3- 1r√4gh3

**Q.**A stone of mass m, tied to the end of a string, is whirled in a horizontal circle in zero gravity. The length of the string is gradually decreased without exerting any external torque. At an instant when the radius of the circle is r, the tension in the string is T=Ar−n, where A is a constant. Find the value of n (integer only)

**Q.**In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to

(ignore viscosity of air)

- r4
- r
- r3
- r2

**Q.**A cylinder initially kept at rest on a horizontal rough surface is given an angular velocity 10 rad/s. What is the distance travelled by the centre of mass of the cylinder till it begins pure rolling ?

Given: Coefficient of kinetic and static frcition are equal (μ=0.5) and radius of cylinder R=3 m. Also, take g=10 m/s2.

- 5 m
- 10 m
- 1 m
- 20 m

**Q.**A circular disc rolls down an inclined plane without slipping. What fraction of its total energy is translational energy?

- 1√2
- 12
- 13
- 23

**Q.**

Two capillary tubes of the same length but different radii r1 and r2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

**Q.**A solid sphere of mass m is kept between two planks rolls moving without slipping with the velocities as shown.

Determine the total kinetic energy of the solid sphere.

- 12mv2
- 45mv2
- 115mv2
- 135mv2

**Q.**A bock of mass m is placed on a frictionless inclined plane of inclination θ. The inclined plane has its base fixed on the floor of a lift which is going up with a constant acceleration a. When the block is released, it will slide down the plane with acceleration

- (g+a)sinθ
- (g−a)sinθ
- (g+a)cosθ
- (g−a)cosθ

**Q.**A uniform thin rod of mass, M=1 kg and length, L=2 m is hinged by a frictionless pivot at its one end O as shown in figure. A bullet of mass, m=50 g moving horizontally with a velocity v=1500 ms−1 strikes the free end of the rod and gets embedded in it the angular velocity of the system about O just after the collision is-

- 98 rad s−1
- 95 rad s−1
- 100 rad s−1
- 76 rad s−1

**Q.**A stationary uniform rod of mass m=1 kg and length l=2 m leans against a smooth vertical wall making an angle θ=45o with rough horizontal floor. Find the frictional force that is exerted by the floor on the rod.

- 15 N
- 5 N
- 10 N
- 20 N

**Q.**By what factor will the flow rate of a viscous fluid through a pipe change, if the pipe radius is doubled, the fluid viscosity is doubled, the length is doubled and the pressure drop is reduced to a quarter of its previous value?

- 16
- 14
- 4
- Doesn't change

**Q.**When water (viscosity, ηw=0.01 poise) and benzene (viscosity, ηb=0.0065 poise) are allowed to flow through a pipe, it was found that the same amount of liquids are collected in the same time but the pressure drop that caused the flow are different. If the pressure drop in water is 0.015 atm, then the pressure drop in benzene will be

- 2.3×10−3 atm
- 975×10−5 atm
- 2.3×10−5 atm
- 4.33×10−3 atm

**Q.**A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical pane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is

- 2g3lcosθ
- 3g2lsinθ
- 2g3lsinθ
- 3g2lcosθ

**Q.**A circular ring of radius R and mass m made of a uniform wire of cross-sectional area A is rotated about a stationary vertical axis passing through its center and perpendicular to the plane of the ring. The breaking stress of the material of the ring is σb. Determine the maximum angular speed ωmax at which the ring may be rotated without failure.

- √πAσbmR
- √πAσb2mR
- √2πAσbmR
- √4πAσbmR

**Q.**An oil with a viscosity of μ and density ρ flows in a pipe of diameter D. The pressure drop ΔP needed to produce a flow rate of Q for laminar flow is given as

ΔP=kQμLD4, L is length of pipe

The value of k is _____.

- 40.74

**Q.**Four identical rods of mass M=6 kg each are welded at their ends to form a square and then welded to a massive ring having mass M=4 kg and radius R=1 m. If the system is allowed to roll down the incline of inclination θ=30∘.

The minimum value of friction coefficient to prevent slipping is

- 57
- 512√3
- 5√37
- 75√3

**Q.**A thin ring of radius R is made of a material of density ρ and Young's modulus Y. If the ring is rotated about its centre in its own plane with angular velocity ω, find the small increase in its radius.

ρω2R2Y

ρω2R3Y

ρωR2Y

ρω3R2Y

**Q.**The volume of a homogenous fluid passing per unit time through a pipe is

- Directly proportional to the fourth power of its internal radius.
- Directly proportional to the pressure difference between its ends.
- All the above
- Inversely proportional to its length and to the viscosity of the fluid.

**Q.**Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg.m2and 10 rad s–1 respectively while those for the second one are 0.2 kg m2 and 5 rad s–1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is

- 103 J
- 203 J
- 53 J
- 23 J

**Q.**What will be the total resistance offered to the flow of water by the system of pipe 1, pipe 2, pipe 3 and pipe ignoring the joints? If all the pipes are of length 3 m and radius 2 m and 'η' is viscosity of water. (Assume π=3)

- 1.25η
- 3η
- 4.5η
- 9η

**Q.**A raindrop of radius 0.2 mm falls through air. If the viscosity of air is 18×10–6 Pl, if the viscous drag acting on the drop when its speed is 1 ms–1 is 67.8×10–p newton, then find p

**Q.**A stationary uniform rod of mass m=1 kg and length l=2 m leans against a smooth vertical wall making an angle θ=45o with rough horizontal floor. Find the frictional force that is exerted by the floor on the rod.

- 5 N
- 10 N
- 20 N
- 15 N

**Q.**Which of the following correctly states how the viscosities of a liquid and a gas will change with temperature?

- Viscosity increases with increase in temperature of a liquid and decreases with the increase in temperature of a gas
- Viscosity increases with increase in temperature of a liquid and increases with the increase in temperature of a gas
- Viscosity decreases with increase in temperature of a liquid and decreases with the increase in temperature of a gas
- Viscosity decreases with increase in temperature of a liquid and increases with the increase in temperature of a gas

**Q.**A solid sphere rolls on a rough horizontal surface with a linear speed 7 m/s and collides elastically with a fixed smooth vertical wall. Then, find the speed of the sphere when it has started pure rolling in the backward direction in m/s.

**Q.**As per the provision of IS 800 : 2007, the shear lag effect in flanges may be disregarded provided :

1.b0≤L020(For outstand elements)2.bi≤L010(For internal elements)3.b0≥L020(For outstand elements)4.b0≥L010(For internal elements)

Which of the above statement are CORRECT ?

- 1 and 4
- 1 and 2
- 2 and 3
- 3 and 4