Laws of Motion NEET Important Questions PDF Download

Q 1 :
A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2 : 2 : 1$ . If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$ , the speed of the third (lighter) fragment is [2022]

$v$
$\sqrt{2} v$
$2 \sqrt{2} v$
$3 \sqrt{2} v$

(3)

Given, mass of the shell = $m$

Ratio of masses of the fragments is 2 : 2 : 1

Therefore, masses of the three fragments are

$m_{1} = \frac{m}{2}, m_{2} = \frac{m}{2}$ and $m_{3} = \frac{m}{4}$

Now fragments with equal masses i.e., $m_{1}$ and $m_{2}$ fly off perpendicularly with speeds $v_{1} = v_{2} = v .$ Let the velocity of third fragment be $v' .$

Applying law of conservation of momentum,

$m_{1} v_{1} \hat{i} + m_{2} v_{2} \hat{j} + m_{3} \vec{v} = 0$

$\frac{m v}{2} \hat{i} + \frac{m v}{2} \hat{j} + \frac{m}{4} \vec{v'} = 0 \Rightarrow \vec{v'} = 2 v (- \hat{i} - \hat{j})$

$| \vec{v} |$ $= 2 v \sqrt{{(- 1)}^{2} + {(- 1)}^{^{2}}} = 2 \sqrt{2} v$

Q 2 :
An object flying in air with velocity $(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity $(100 \hat{i} + 35 \hat{j} + 8 \hat{k}) .$ The velocity of the larger piece will be: [2019]

$4 \hat{i} + 23 \hat{j} - 16 \hat{k}$
$- 100 \hat{i} - 35 \hat{j} - 8 \hat{k}$
$20 \hat{i} + 15 \hat{j} - 80 \hat{k}$
$- 20 \hat{i} - 15 \hat{j} - 80 \hat{k}$

(1)

From the law of conservation of linear momentum $m \vec{v} = m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}$

$\Rightarrow 6 k (20 \hat{i} + 25 \hat{j} - 12 \hat{k}) = k (100 \hat{i} + 35 \hat{j} + 8 \hat{k}) + 5 k {\vec{v}}_{2}$

$\Rightarrow 5 {\vec{v}}_{2} = (120 - 100) \hat{i} + (150 - 35) \hat{j} + (- 72 - 8) \hat{k}$

$\Rightarrow 5 {\vec{v}}_{2} = 20 \hat{i} + 115 \hat{j} - 80 \hat{k} \Rightarrow {\vec{v}}_{2} = 4 \hat{i} + 23 \hat{j} - 16 \hat{k}$

Topic Question Set

Q 1 :
A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2 : 2 : 1$ . If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$ , the speed of the third (lighter) fragment is [2022]

Q 2 :
An object flying in air with velocity $(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity $(100 \hat{i} + 35 \hat{j} + 8 \hat{k}) .$ The velocity of the larger piece will be: [2019]

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Topic Question Set

Q 1 : A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2:2:1. If the fragments having equal mass fly off along mutually perpendicular directions with speed v, the speed of the third (lighter) fragment is [2022]

Q 2 : An object flying in air with velocity (20i^+25j^-12k^) suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity (100i^+35j^+8k^). The velocity of the larger piece will be: [2019]

Want Us to Email you About Special Offers & Updates?

Q 1 :
A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2 : 2 : 1$ . If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$ , the speed of the third (lighter) fragment is [2022]

Q 2 :
An object flying in air with velocity $(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity $(100 \hat{i} + 35 \hat{j} + 8 \hat{k}) .$ The velocity of the larger piece will be: [2019]