SATHEE: Work Energy And Power Question 122

Work Energy And Power Question 122

Question: Two particles having position vectors $\vec{r_{1}} = (3 \hat{i} + 5 \hat{j})$ metres and $\vec{r_{2}} = (- 5 \hat{i} - 3 \hat{j})$ metres are moving with velocities ${\vec{v}}_{1} = (4 \hat{i} + 3 \hat{j}) m / s$ and ${\vec{v}}_{2} = (α \hat{i} + 7 \hat{j})$

$m / s .$ If they collide after 2 seconds, the value of $‘ α^{'}$ is [EAMCET 2003]

Options:

A) 2

B) 4

C) 6

D) 8

Show Answer

Answer:

Correct Answer: D

Solution:

It is clear from figure that the displacement vector $Δ \vec{r}$

between particles $p_{1}$ and $p_{2}$ is $Δ \vec{r} = \vec{r_{2}} - \vec{r_{1}} = - 8 \hat{i} - 8 \hat{j}$

$| Δ \vec{r} | = \sqrt{{(- 8)}^{2} + {(- 8)}^{2}} = 8 \sqrt{2}$ …(i)

Now, as the particles are moving in same direction $(∵ \vec{v_{1}} and \vec{v_{2}} are + v e)$ ,

the relative velocity is given by ${\vec{v}}_{r e l} = \vec{v_{2}} - \vec{v_{1}} = (α - 4) \hat{i} + 4 \hat{j}$

${\vec{v}}_{r e l} = \sqrt{{(α - 4)}^{2} + 16}$ …(ii)

Now, we know $| {\vec{v}}_{r e l} | = \frac{| Δ \vec{r} |}{t}$

Substituting the values of ${\vec{v}}_{r e l}$ and $| Δ \vec{r} |$ from equation (i) and (ii) and $t = 2 s$ , then on solving we get $α = 8$

Work Energy And Power Question 122

Question: Two particles having position vectors $\vec{r_{1}} = (3 \hat{i} + 5 \hat{j})$ metres and $\vec{r_{2}} = (- 5 \hat{i} - 3 \hat{j})$ metres are moving with velocities ${\vec{v}}_{1} = (4 \hat{i} + 3 \hat{j}) m / s$ and ${\vec{v}}_{2} = (α \hat{i} + 7 \hat{j})$

Options:

Answer:

Solution:

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Work Energy And Power Question 122

Question: Two particles having position vectors r1→=(3i^+5j^) metres and r2→=(−5i^−3j^) metres are moving with velocities v→1=(4i^+3j^)m/s and v→2=(αi^+7j^)

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: Two particles having position vectors $\vec{r_{1}} = (3 \hat{i} + 5 \hat{j})$ metres and $\vec{r_{2}} = (- 5 \hat{i} - 3 \hat{j})$ metres are moving with velocities ${\vec{v}}_{1} = (4 \hat{i} + 3 \hat{j}) m / s$ and ${\vec{v}}_{2} = (α \hat{i} + 7 \hat{j})$