Previous Years GATE Questions on Dynamics 2001-2004

Solved GATE Questions on Dynamics

Question 1. Mass M slides in a frictionless slot in the horizontal direction and the bob of the mass m is hinged to mass M at C, through a rigid massless rod. The system is released from rest with , the velocities of  and  can be determined using the fact that, for the system (i.e., m and M together),

(A) the linear momentum in X and Y directions are conserved but the energy is not conserved.

(B) the linear momentum in X and Y directions are conserved and the energy is also conserved

(C) the linear momentum in X  direction is conserved and the energy is also conserved

(D) the linear momentum in Y direction is conserved and the energy is also conserved

GATE-ME-2001

Hint

Question 2. A participle P is projected from the earth surface at latitude 45 with escape velocity . The velocity direction makes an angle  with the local vertical. The particle will escape the earth’s gravitational field.

(A) Only when 

(B) Only when 

(C) Only when 

(D) Irrespective of the value of

GATE-ME-2001

Hint

Question 3. In the figure shown, the spring deflects by  to position A (the equilibrium position) when a mass m is kept on it, During free vibration, the mass is at position B at some instant. The change in potential energy of the spring-mass system from position A to position B is

(A) ½ kx²

(B) ½ kx²-mgx

(C) ½ k(x+)²

(D) ½ kx²+mgx

GATE-ME-2001

Hint

Data for Q.4-5 are given below. Solve the problems and choose correct answers

A reel of mass “m” and radius of gyration “K” is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. Consider the thickness of the thread and its mass negligible in comparison with the radius “r” of the hub and the reel mass “m”. Symbol “g” represents the acceleration due to gravity.

GATE-ME-2001

Question 4. The linear acceleration of the reel is

(A) gr²/(r²+k²)

(B) gk²/(r²+k²)

(C) grk/(r²+k²)

(D) mgr²/(r²+k²)


Hint

Question 5. The tension in the thread is

(A) mgr²/(r²+k²)

(B) mgrk²/(r²+k²)

(C) mgk²/(r²+k²)

(D) mg/(r²+k²)


Hint

Question 6. A bullet of mass “m” travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of mass “M” initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance “S” along the floor. Assuming  to be the coefficient of kinetic friction between the block and the floor and “g” the acceleration due to gravity. What is the velocity v of the bullet?

(A) 

(B)

(C)

(D) 

GATE-ME-2001

Hint

Question 7. A rigid body shown in the Fig, (a) has a mass of 10 kg. It rotates with a uniform angular velocity ‘w’. A balancing mass of 20 kg is attached as shown in Fig.(b). The percentage increase in mass moment of inertia as a result of this addition is

(a)                                          (b)

(A) 25 %

(B) 50 %

(C) 100%

(D) 200 %

GATE-ME-2004

Hint

Question 8.  An ejector mechanism consists of a helical compression spring having a spring constant of K=981x 103 N/m. It is pre-compressed by 100 mm from its free state. If it is used to eject a mass of 100 kg held on it, the mass will move up through a distance of

(A) 100mm

(B) 500mm

(C) 981mm

(D) 1000 mm

GATE-ME-2004

Hint

Question 9. A uniform stiff rod-of length 300 mm and having a weight of 300 N is pivoted at one end and connected to a spring at the other end. For keeping the rod vertical in a stable position the minimum value of spring constant K needed is

(A) 300 N/m

(B) 400 N/m

(C) 500 N/m

(D) 1000 N/m

GATE-ME-2004

Hint

Answer Keys