1
GATE ME 2024
Numerical
+2
-1.33

A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of $P = 100$ kN and $Q = 50$ kN. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is _________ kN (rounded off to 1 decimal place).

2
GATE ME 2023
+2
-0.66

A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?

Take the acceleration due to gravity to be 𝑔 = 9.8 m/s2. Options have been rounded off to one decimal place.

A
19.6 𝒊̂
B
19.6 𝒋̂
C
17.0 𝒊̂+ 9.8 𝒋̂
D
9.8 𝒊̂+ 17.0 𝒋̂
3
GATE ME 2017 Set 2
Numerical
+2
-0
The rod PQ of length L = 2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s2 . The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML2 /12). At this instant, the magnitude of angular acceleration (in radian/s2 ) of the rod is ____________.
4
GATE ME 2017 Set 1
+2
-0.6
Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is.
A
$$\sqrt {{3 \over 4}}$$
B
$$\sqrt {{3 \over 2}}$$
C
$$1$$
D
$$\sqrt 2$$
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