A glass wind screen whose inclination with the vertical can be ch… - Vidyadip

MCQ

A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of $2\,\,m/s$. At what angle $\alpha$ with the vertical should the wind screen be placed so that the rain drops falling vertically downwards with velocity $6\,\, m/s$ strike the wind screen perpendicularly.

✓
$tan^{-1}(3)$
B
$tan^{-1}(1/3)$
C
$cos^{^{-1}}(3)$
D
$sin^{-1}(1/3)$

✓

Answer

Correct option: A.

$tan^{-1}(3)$

a
Let vertical direction limit vector be $j,$ horizontal

$\mathrm{V}_{\mathrm{car}}=2 \hat{\mathrm{i}}$

$V_{\text {drops }}=6 \hat{j}$

$\mathrm{V}_{\text {drops }} \mathrm{W} .$ $r.t$ car $=\mathrm{V}_{\text {drops }}-\mathrm{V}_{\text {car }}$

$=-2 \hat{i}+6 \hat{j}$

$\cos \theta_{1}=\frac{\hat{j} \cdot(-2 \hat{i}+6 \hat{j})}{|\hat{j}| \cdot|-2 \hat{i}+6 \hat{j}|}$

$=\frac{6}{\sqrt{2^{2}+6^{2}} \cdot 1}=\frac{6}{\sqrt{40}}$

$\Rightarrow \cos \theta_{1}=\frac{3}{\sqrt{10}}$

$\Rightarrow \sin \theta_{2}=\frac{3}{\sqrt{10}}$

$\Rightarrow \tan \theta_{2}=3$

$\Rightarrow \theta_{2}=\tan ^{-1} 3$

Hence wind stream is inclined at tan $^{-1} 3^{\circ}$ with vertical.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3.2 , motion in plane→3.2 , motion in plane — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A wire has a mass $0.3 \pm 0.003\text{g},$ radius $0.5 \pm 0.005\text{mm}$ and length $6 \pm 0.06\text{cm}.$ The maximum percentage error in the measurement of its density is

A man of mass 60kg and a boy of mass 30kg are standing together on frictionless ice surface. If they push each other apart man moves away with a speed of 0.4m/ s relative to ice. After 5sec they will be away from each other at a distance of.

A constant force $F = m_2g/2$ is applied on the block of mass $m_1$ as shown in fig. The string and the pulley are light and the surface of the table is smooth. The acceleration of $m_1$ is

Force acts for $20\,s$ on a body of mass $20\,kg$, starting from rest, after which the force ceases and then body describes $50\,m$ in the next $10\,s$. The value of force will be $..........\,N$

A particle initially at rest is subjected to two forces. One is constant, the other is a retarding force proportional to the particle velocity. In the subsequent motion of the particle :

A satellite is moving around the earth with speed $v$ in a circular orbit of radius $r$. If the orbit radius is decreased by $1\%$, its speed will

Two particles $A$ and $B$, move with constant velocities ${\vec v_1}$ and ${\vec v_2}$. At the initial moment their position vectors are ${\vec r_1}$ and ${\vec r_2}$ respectively. The condition for their collision is

The amount of radiation emitted by a perfectly black body is proportional to

One mole of a perfect gas in a cylinder fitted with a piston has a pressure $P,$ volume $V$ and temperature $T.$ If the temperature is increased by $1 \,K$ keeping pressure constant, the increase in volume is

A man does a given amount of work in $ 10 sec.$ Another man does the same amount of work in $20 sec.$ The ratio of the output power of first man to the second man is