Question 557

Which one of the following statements is incorrect?

Rolling friction is smaller than sliding friction.

Limiting value of static friction is directly proportional to normal reaction.

Coefficient of sliding friction has dimensions of length.

Frictional force opposes the relative motion.

Solution

C.

Coefficient of sliding friction has dimensions of length.

Coefficient of friction or sliding friction has no dimension.

$f={\mu}_{s}N\phantom{\rule{0ex}{0ex}}\Rightarrow {\mu}_{s}=\frac{f}{N}=\left[{M}^{0}{L}^{0}{T}^{0}\right]$

Question 558

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

0.5

0.25

0.4

0.8

Solution

B.

0.25

According to law of conservation of linear momentum,

mv + 4m x 0 = 4mv' + 0

$v\text{'}=\frac{v}{4}\phantom{\rule{0ex}{0ex}}e=\frac{relativevelocityofseparation}{Relativevelocityofapproach}=\frac{{\displaystyle \frac{v}{4}}}{v}\phantom{\rule{0ex}{0ex}}e=\frac{1}{4}=0.25$

Question 559

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 an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is

$a=\frac{g}{\mathrm{cos}ec\theta}$

$a=\frac{g}{\mathrm{sin}\theta}$

a = g tan θ

a = g cos θ

Solution

C.

a = g tan θ

In non-inertial frame,

N sin θ = ma ...(i)

N cos θ = mg... (ii)

tan θ = a/g

a = g tan θ

Question 560

A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is p0 and temperature is T0, atmospheric pressure is also p_{0}. Now, the temperature of the gas is increased to 2T_{0}, the tension of the wire will be

2p

_{0}Ap

_{0}Ap

_{0}A/24p

_{0}A

Solution

B.

p_{0}A

The volume of the gas is constant i.e., V = constant

∴ p ∝ T i.e pressure will be doubled if the temperature is doubled.

Let F be the tension in the wire. Then, the equilibrium of anyone pipes gives.

$\mathrm{F}=(\mathrm{p}-{\mathrm{p}}_{0})\mathrm{A}=2({\mathrm{p}}_{0}-{\mathrm{p}}_{0})={\mathrm{p}}_{0}\mathrm{A}$