1
JEE Advanced 2024 Paper 1 Online
+3
-1

A block of mass $5 \mathrm{~kg}$ moves along the $x$-direction subject to the force $F=(-20 x+10) \mathrm{N}$, with the value of $x$ in metre. At time $t=0 \mathrm{~s}$, it is at rest at position $x=1 \mathrm{~m}$. The position and momentum of the block at $t={\pi \over 4} \mathrm{s}$ are

A
$-0.5 \mathrm{~m}, 5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
B
$0.5 \mathrm{~m}, 0 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
C
$0.5 \mathrm{~m},-5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
D
$-1 \mathrm{~m}, 5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
2
JEE Advanced 2013 Paper 1 Offline
+2
-0.5
A particle of mass m is projected from the ground with an initial speed u0 at an angle $$\alpha$$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is
A
$${\pi \over 4}$$
B
$${\pi \over 4} + \alpha$$
C
$${\pi \over 2} - \alpha$$
D
$${\pi \over 2}$$
3
IIT-JEE 2011 Paper 2 Offline
+3
-0.75

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the center of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is

A
250 m/s
B
$$250\sqrt 2$$ m/s
C
400 m/s
D
500 m/s
4
IIT-JEE 2009 Paper 1 Offline
+3
-1

Look at the drawing given in the figure below which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is $$m$$. the mass of the ink used to draw the outer circle is $$6m$$. The coordinates of the centres of the different parts are: outer circle (0, 0), left inner circle ($$-a,a$$), right inner circle ($$a,a$$), vertical line (0, 0) and horizontal line ($$0,-a$$). The y-coordinate of the centre of mass of the ink in this drawing is

A
$$\frac{a}{10}$$
B
$$\frac{a}{8}$$
C
$$\frac{a}{12}$$
D
$$\frac{a}{3}$$
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