1
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A particle of mass m is projected with a speed u from the ground at an angle $$\theta = {\pi \over 3}$$ w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $$u\widehat i$$ . The horizontal distance covered by the combined mass before reaching the ground is:
A
$$2\sqrt 2 {{{u^2}} \over g}$$
B
$${{3\sqrt 3 } \over 8}{{{u^2}} \over g}$$
C
$${{3\sqrt 2 } \over 4}{{{u^2}} \over g}$$
D
$${5 \over 8}{{{u^2}} \over g}$$
2
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
Two particles of equal mass m have respective
initial velocities $$u\widehat i$$ and $$u\left( {{{\widehat i + \widehat j} \over 2}} \right)$$.
They collide completely inelastically. The energy lost in the process is :
A
$${1 \over 3}m{u^2}$$
B
$${1 \over 8}m{u^2}$$
C
$${3 \over 4}m{u^2}$$
D
$$\sqrt {{2 \over 3}} m{u^2}$$
3
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $$\sqrt {2gh}$$. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $$\sqrt {{h \over g}}$$ is :
A
$$\sqrt {{1 \over 2}}$$
B
$${1 \over 2}$$
C
$$\sqrt {{3 \over 2}}$$
D
$$\sqrt {{3 \over 4}}$$
4
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be :
A
$$\left( {{{\sqrt 3 } \over 4}m,{5 \over {12}}m} \right)$$
B
$$\left( {{7 \over {12}}m,{{\sqrt 3 } \over 8}m} \right)$$
C
$$\left( {{7 \over {12}}m,{{\sqrt 3 } \over 4}m} \right)$$
D
$$\left( {{{\sqrt 3 } \over 8}m,{7 \over {12}}m} \right)$$
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