1
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1

In the given figure, the angles $\angle B A Q=\angle C P Q=\angle C B Q=\frac{\pi}{2}$; and the lengths $Q A=3$ units, $A B=$ 4 units, and $B C=1$ unit. What is the length of $P Q$ ?

IAT (IISER) 2024 Mathematics - Properties of Triangles Question 1 English
A
2 unit
B
2.2 unit
C
$\sqrt{2}$ unit
D
$3-\sqrt{2}$ unit
2
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a point. Abhijit moves with a constant speed. Vani starts with a constant acceleration from rest. They meet again on the track with the same speed. Which of the following is correct?
A
Abhijit travelled the same distance travelled by Vani.
B
Abhijit travelled half the distance travelled by Vani.
C
Abhijit travelled double the distance travelled by Vani.
D
Abhijit travelled $4 / 3$ of the distance travelled by Vani.
3
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1

Consider a simple pendulum undergoing simple harmonic motion with a time period $T$, and a fixed amplitude $\theta_0$ of angular oscillation. Its angular momentum about the point of suspension exhibits an oscillatory behaviour with an amplitude $A$. Which of the following relations between $A$ and $T$ is correct?

A
$A \propto T^1$
B
$A \propto T^2$
C
$A \propto T^3$
D
$A \propto T^4$
4
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
An inextensible cord of negligible mass passes over the rim of a solid disc of mass $M$ and radius $R$. The disc is free to rotate about an axis passing through the centre perpendicular to the plane of the screen, as shown in the figure. Two blocks of masses $M$ and $\widetilde{M} / 2$ are attached to the two free ends of the cord. Assume that there is no slipping of the cord on the disc. The acceleration due to gravity is $g$. What is the value of the angular acceleration of the disc? IAT (IISER) 2024 Physics - Rotational Motion Question 1 English
A
$g / R$
B
$g / 2 R$
C
$g / 3 R$
D
$g / 4 R$
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