New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Motion in A Straight Line question

2019 · 12 Jan · Shift 1 · Q71

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Motion in A Straight Line
2019 · 12 Jan · Shift 1 · Q71

Motion in A Straight Line question

2019 · 12 Jan · Shift 1 · Q71

JEE MainPhysicsMotion in A Straight LineMCQ+4 / −1

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction , and (ii) in the opposite direction is :

A
${{25} \over {11}}$
B
${3 \over 2}$
C
${{11} \over 5}$
D
${5 \over 2}$

View written solutionFree

Correct answer: C

Given data

Length of passenger train: $L_1 = 60\,\text{m}$
Speed of passenger train: $v_1 = 80\,\text{km/h}$
Length of freight train: $L_2 = 120\,\text{m}$
Speed of freight train: $v_2 = 30\,\text{km/h}$

To completely cross each other, the total distance to be covered in relative motion is

$L = L_1 + L_2 = 60 + 120 = 180\,\text{m}$

Case (i): Same direction

Relative speed:

$v_{\text{same}} = 80 - 30 = 50\,\text{km/h}$

So time taken is

$t_1 = \frac{180}{50}$

Case (ii): Opposite direction

Relative speed:

$v_{\text{opp}} = 80 + 30 = 110\,\text{km/h}$

So time taken is

$t_2 = \frac{180}{110}$

Required ratio

$t_1 : t_2 = \frac{180}{50} : \frac{180}{110}$

Cancel $180$ :

$t_1 : t_2 = \frac{1}{50} : \frac{1}{110} = 110 : 50 = 11 : 5$

Hence,

$\frac{t_1}{t_2} = \frac{11}{5}$

Check options

A: $\frac{25}{11}$
B: $\frac{3}{2}$
C: $\frac{11}{5}$ ✅
D: $\frac{5}{2}$

Therefore, the correct option is C.

More from Motion in A Straight Line

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in $15 s$ and (ii) the time at which the car will catch up with the scooter are,… Includes diagram2018 · MCQ
An automobile, travelling at $40$ km/h, can be stopped at a distance of $40$ m by applying brakes. If the same automobile is travelling at $80$ km/h, the minimum stopping distance, in metres, is (assume no skidding) :2018 · MCQ
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.2018 · MCQ
Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?2017 · MCQ
A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2 . The car will catch up…2017 · MCQ
A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?2017 · MCQ
Two stones are thrown up simultaneously from the edge of a cliff $240 m$ high with initial speed of $10 m / s$ and $40 m / s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone…2015 · MCQ
From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:2014 · MCQ