1
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

Two bodies of mass $$1 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ have position vectors $$\hat{i}+2 \hat{j}+\hat{k}$$ and $$-3 \hat{i}-2 \hat{j}+\hat{k}$$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

A
$$\hat{i}+2 \hat{j}+\hat{k}$$
B
$$-3 \hat{i}-2 \hat{j}+\hat{k}$$
C
$$-2 \hat{i}+2 \hat{k}$$
D
$$2 \hat{i}-\hat{j}+2 \hat{k}$$
2
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

In two different experiments, an object of mass $$5 \mathrm{~kg}$$ moving with a speed of $$25 \mathrm{~ms}^{-1}$$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

A
Impulse and average force acting on the object will be same for both the cases.
B
Impulse will be same for both the cases but the average force will be different.
C
Average force will be same for both the cases but the impulse will be different.
D
Average force and impulse will be different for both the cases.
3
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

A body of mass $$10 \mathrm{~kg}$$ is projected at an angle of $$45^{\circ}$$ with the horizontal. The trajectory of the body is observed to pass through a point $$(20,10)$$. If $$\mathrm{T}$$ is the time of flight, then its momentum vector, at time $$\mathrm{t}=\frac{\mathrm{T}}{\sqrt{2}}$$, is _____________.

[Take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$ ]

A
$$100 \hat{i}+(100 \sqrt{2}-200) \hat{j}$$
B
$$100 \sqrt{2} \hat{i}+(100-200 \sqrt{2}) \hat{j}$$
C
$$100 \hat{i}+(100-200 \sqrt{2}) \hat{j}$$
D
$$100 \sqrt{2} \hat{i}+(100 \sqrt{2}-200) \hat{j}$$
4
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

A ball of mass $$0.15 \mathrm{~kg}$$ hits the wall with its initial speed of $$12 \mathrm{~ms}^{-1}$$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $$100 \mathrm{~N}$$, calculate the time duration of the contact of ball with the wall.

A
0.018 s
B
0.036 s
C
0.009 s
D
0.072 s
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