1
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
$$100 \sqrt{2} \hat{i}+(100 \sqrt{2}-200) \hat{j}$$
2
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
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1 A body of mass $$8 \mathrm{~kg}$$ and another of mass $$2 \mathrm{~kg}$$ are moving with equal kinetic energy. The ratio of their respective momentum will be :

A
1 : 1
B
2 : 1
C
1 : 4
D
4 : 1
4
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1 Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms$$-$$1 collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?

A
100 N
B
200 N
C
300 N
D
400 N
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