1
JEE Advanced 2023 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height $3 h$ from the ground, as shown in the figure. A spherical ball of mass $m$ is released on the slide from rest at a height $h$ from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_0=u_0 \hat{x}$ and falls on the ground at a distance $d$ from the building making an angle $\theta$ with the horizontal. It bounces off with a velocity $\vec{v}$ and reaches a maximum height $h_1$. The acceleration due to gravity is $g$ and the coefficient of restitution of the ground is $1 / \sqrt{3}$. Which of the following statement(s) is(are) correct? A
$\overrightarrow{\mathrm{u}}_0=\sqrt{2 g h} \hat{x}$
B
$\vec{v}=\sqrt{2 g h}(\hat{x}-\hat{z})$
C
$\theta=60^{\circ}$
D
$d / h_1=2 \sqrt{3}$
2
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2 Starting at time t = 0 from the origin with speed 1 ms-1, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation $$y = {{{x^2}} \over 2}$$. The x and y components of its acceleration are denoted by ax and ay, respectively. Then
A
ax = 1 ms-2 implies that when the particle is at the origin, ay = 1 ms-2
B
ax = 0 implies ay = 1 ms-2 at all times
C
at t = 0, the particle's velocity points in the x-direction
D
ax = 0 implies that at t = 1s, the angle between the particle's velocity and the x axis is 45$$^\circ$$
3
IIT-JEE 1999 Screening
MCQ (More than One Correct Answer)
+3
-0.75
The coordinates of a particle moving in a plane are given by x(t) = a cos(pt) and y(t) = b sin(pt) where a, b (< a) and p are positive constants of approprite dimensions. Then
A
the path of the particle is an ellipse
B
the velocity and acceleration of the particle are normal to each other at t = $${\pi \over {2p}}$$
C
the acceleration of the particle is always directed towards a focus
D
the distance traveled by the particle in time interval t = 0 to t = $${\pi \over {2p}}$$ is a
4
IIT-JEE 1993
MCQ (More than One Correct Answer)
+2
-0.5
A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest at t = 1 at the point x = 1. NO other information is available about its motion at intermediate times ( 0 < t < 1 ). If $$\alpha$$ denotes the instantaneous acceleration of the particle, then:
A
$$\alpha$$ cannot remain positive for all t in the interval $$0 \le t \le 1$$
B
$$\left| \alpha \right|$$ cannot exceed 2 at any point in its path.
C
$$\left| \alpha \right|$$ must be $$\ge$$ 4 at some point or points in its path.
D
$$\alpha$$ must be change sign during the motion, but no other assertion can be made with the information given.
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