Question 549

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current ‘I’ along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire ‘B’ is given by

Solution

D.

Force between BC and AB will be same in magnitude.

Question 550

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to

3D/2

D

5D/4

7D/5

Solution

C.

5D/4

As track is frictionless, so total mechanical energy will remain constant,

$i.e.,0+mgh=\frac{1}{2}m{v}_{L}^{2}+0\phantom{\rule{0ex}{0ex}}u\mathrm{sin}g{v}^{2}-{u}^{2}=2gh,\phantom{\rule{0ex}{0ex}}h=\frac{{v}_{L}^{2}}{2g}(\because u=0)\phantom{\rule{0ex}{0ex}}Forcompletingtheverticalcircle{V}_{L}\ge \sqrt{5gR}\phantom{\rule{0ex}{0ex}}or,h=\frac{5gR}{2g}=\frac{5}{2}R=\frac{5}{4}D$

Question 551

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 552

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

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