Solved GATE Questions on Dynamics
Question 1. A circular disc of radius R rolls without slipping at a velocity v. The magnitude of the velocity at point P (see figure) is
(A) 
v
(B)
v/2
(C) v/2
(D) 2v/
GATE-ME-2008
Hint 1. (Ans A)
The instantaneous centre of rotation of disc is 0, i.e. its point of contact with ground every other point on the disc is rotating with respect to this centre with an angular velocity.
Question 2. A cantilever type gate hinged at Q is shown in the figure. P and R are the centres of gravity of the cantilever part and the counterweight respectively. The mass of the cantilever part
is 75 kg. The mass of the counterweight, for static balance, is
(A) 75 kg
(B) 150 kg
(C) 225 kg
(D) 300 kg
GATE-ME-2008
Hint 2. (Ans D)
For balancing the moments about the hinge Q,
Question 3. A straight rod of length L(t), hinged at one end and freely extensible at, the other end,
rotates through an angle 
about the hinge. At time t, L(t)=1m, L (t)=1m/s, 
rad and 
rad/s.The magnitude of the velocity at the other end of the rod is
(A) 1 m/s
(B) 
m/s
(C) 
m/s
(D) 2 m/s
GATE-ME-2008
Increase in length of the rod
New length 
Tangential velocity 
Resultant velocity
Question 4. A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of 2L/3 from the hinge so that the rod swings to
the right. The reaction at the hinge is
(A) –P
(B) 0
(C) P/3
(D) 2P/3
GATE-ME-2009
Hint 4. (Ans B)
Assume reaction at hinge is R,
Torque, 
Linear acceleration
Governing Equation,
Question 5. There are two points P and Q on a planar rigid body. The relative velocity between the two
points
(A) Should always be along PQ
(B) Can be oriented along any direction
(C) Should always be perpendicular to PQ
(D) Should be along QP when the body undergoes pure translation
GATE-ME-2010
Hint 5. (Ans C)
Question 6.A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force Fx (in N) exerted by the rubber band as a function of distance x (in m) is given by Fx = 300x2. If the stone is displaced by 0.1 m from the un-stretched position (x = 0) of the rubber band, the energy stored in the rubber band is
(A) 0.01 J
(B) 0.1 J
(C) 1 J
(D) 10 J
GATE-ME-2011
Hint 6. (Ans B)
Energy stored =work done=
Question 7. The coefficient of restitution of a perfectly plastic impact is
(A) 0
(B) 1
(C) 2
(D) 
GATE-ME-2011
Hint 7. (Ans A)
For perfectly plastic collision, co-efficient of restitution =0
Question 8. A link OB is rotating with a constant angular velocity of 2 rad/s in counter clock wise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s respect to the rod, as shown in the figure below. If OA = 1 m , the magnitude of the absolute acceleration of the block at location A in m/s2 is
(A) 3
(B) 4
(C) 5
(D) 6
GATE-ME-2013
Hint 8 (Ans C)
In polar coordinates
Question 9.A pin jointed uniform rigid rod of weight Wand length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is
(A) Zero
(B) W/2
(C) W/4
(D) W
GATE-ME-2013
Hint 9. (Ans C)
It undergoes fixed body rotation about O.
By 1 and 2,
1. (A), 2. (D), 3. (D), 4. (B), 5. (C), 6. (B), 7. (A), 8. (C), 9. (C)