MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

The 'e' Equation

Two point mas...

Question

Two point masses $1$ and $2$ move with uniform velocities $v_{1}$ and $v_{2}$ respectively. Their initial position vectors are $r_{1}$ and $r_{2}$ , respectively. Which of the following should be satisfied for the collision of the point masses?

A

\frac{r_{1} - r_{2}}{| r_{2} - r_{1} |} = \frac{v_{1} - v_{2}}{| v_{2} - v_{1} |}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

\frac{r_{2} - r_{1}}{| r_{1} - r_{1} |} = \frac{v_{2} - v_{1}}{| v_{2} - v_{1} |}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\frac{r_{2} - r_{1}}{| r_{2} + r_{1} |} = \frac{v_{2} - v_{1}}{| v_{2} + v_{1} |}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{r_{2} + r_{1}}{| r_{2} + r_{1} |} = \frac{v_{2} - v_{1}}{| v_{2} + v_{1} |}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{r_{1} - r_{2}}{| r_{2} - r_{1} |} = \frac{v_{1} - v_{2}}{| v_{2} - v_{1} |}$
For collision, $r_{1} + v_{1} t = r_{2} + v_{2} t$
$\Rightarrow r_{1} - r_{2} = (v_{2} - v_{1}) t$
Equating unit vectors, we get
$\frac{r_{1} - r_{2}}{| r_{2} - r_{1} |} = \frac{v_{1} - v_{2}}{| v_{2} - v_{1} |}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Two particles 'A' and 'B', move with constant velocities

_{1}

_{2}

respectively. At the initial moment, their position vectors are

_{1}

_{2}

respectively. The condition for particle 'A' and 'B' for their collision is

Q. The emf (V) and internal resistance (

r

) of a single battery which is equivalent to a parallel combination of two batteries of emf's

V_{1}

V_{2}

and internal resistance

r_{1}

r_{2}

, respectively, with polarities as shown in the figure are given by

\frac{V_{1} r_{2} - V_{2} r_{1}}{r_{1} + r_{2}}, \frac{r_{1} r_{2}}{r_{1} + r_{2}}

.

Q. Two planets are revolving around the Earth with velocities

v_{1}, v_{2}

r_{1}

r_{2}

r_{1} > r_{2}

) respectively. Then

Two satellites of masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ are revolving round the earth in circular orbits of radius $r_{1}$ and $r_{2} (r_{1} > r_{2})$ respectively. Which of the following statements is true regarding their speeds $v_{1}$ and $v_{2}$ ?

Q. Two planets of same density and with radii

R_{1}

R_{2}

R_{1} = 2 R_{2}

have gravitation fields on the surface

g_{1}

g_{2}

and escape velocities

v_{1}

v_{2}

respectively. Then find the value of

\frac{v_{1}}{v_{2}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Realistic Collisions

PHYSICS

Watch in App

explore_more_icon

Explore more

The 'e' Equation

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon