Engineering Sciences
GATE XE topic:mechanics-rigid-bodies PYQs
Build your understanding with focused practice from past exam papers.
Questions 31–40 of 72. Imported answers require independent review unless marked reviewed.
Question 70
Open questionXE-DMCQ1 markNeeds review
End
of the 2 m long rigid rod
is constrained to move horizontally in the slot shown in the figure and has a velocity of 1.0
m/s. The angular velocity of the rod at the instant shown is 2 rad/s. The unit vectors along
and
directions are denoted respectively as
and
. The velocity of point
in m/s is then given by 
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Open questionXE-DMCQ1 markNeeds review
The assembly of four masses connected by rigid mass-less rods is kept on a smooth horizontal floor as shown in the figure. Under the applied force
, the magnitude of angular acceleration of the assembly at the instant shown is 
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 72
Open questionXE-DMCQ1 markNeeds review
A particle is constrained to move at a constant speed on an inclined plane (ABCD) along the curved path shown in the figure. Edges AD and BC are parallel to the
axis. The inclined plane makes an angle
with the
-plane. The velocity vector of the particle makes an angle
with the dotted line which is parallel to edge
. If the speed of the particle is 2 m/s,
, and
, then the
-component of the velocity of the particle in m/s is __________ 
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Open questionXE-DMCQ2 marksNeeds review
The beam in the figure is subjected to a moment
at mid span as shown. Which of the following is the vertical reaction at B? 
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Open questionXE-DMCQ2 marksNeeds review
One end of a uniform rigid rod
of length
and mass
is attached to a frictionless hinge at
. The other end of the rod is connected to the roof at
with a mass-less inextensible thread
. Initially the rod is horizontal and at rest. The gravity is acting vertically downwards as shown. Immediately after the thread
is cut, the reaction on the rod at
is 
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 80
Open questionXE-DMCQ2 marksNeeds review
A mass
kg is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is 10 m/s
and that static and kinetic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is
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Open questionXE-DNAT2 marksNeeds review
The frame shown in the figure is subjected to a uniformly distributed load of 1000 N/m over a distance of 0.6 m. Neglecting the weight of the frame, the maximum shear force (in N) in the region between the supports
and
of the frame is
______.
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Open questionXE-DNAT2 marksNeeds review
A slider moving in a frictionless slot is connected with a linear spring
as shown in the figure. The following is known: stiffness of the spring = 2 kN/m, mass of the slider = 10 kg, and the unstretched length of the spring = 1 m. If the slider is released from rest at
the magnitude of its velocity (in m/s) when it passes through point
is __________ (rounded off to the nearest integer)
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Open questionXE-DNAT2 marksNeeds review
A sphere
of mass
is thrown into the air at 50 m/s along a direction
up from the horizontal. At the topmost point of its trajectory, it has a central (non-oblique) collision with another sphere
which is at rest on top of a vertical pole. Sphere
has a mass of
. Acceleration due to gravity is 10 m/s
. Neglect contact friction and air-resistance. If the coefficient of restitution is 0.3, then the speed (in m/s) of sphere
immediately after the collision is ________ (rounded off to one decimal place)Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 84
Open questionXE-DNAT2 marksNeeds review
The truck shown in the figure is moving on a horizontal road at a speed of 20 m/s. It is carrying a box of mass 100 kg, which is simply placed on the truck platform. The coefficient of friction between the truck platform and the box is 0.25. Take acceleration due to gravity as 10 m/s
. Assume uniform deceleration during braking, and the coefficients of static and kinetic friction to be the same. The shortest distance in meters in which the truck can be brought to rest without the box slipping is
______(round off to the nearest integer)
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