Engineering Mechanics - GATE practice papers - Mechanical

1)   Two velocities are moving in such direction that the angle between them is 30°. The two velocities are having magnitudes 15 m/s and 25 m/s respectively. Calculate the magnitude of resultant velocity. (Marks: 02)
- Published on 19 Oct 15

a. 30.47 m/s
b. 35 m/s
c. 38.72 m/s
d. none of the above
Answer  Explanation 

ANSWER: 38.72 m/s

Explanation:
By using parallelogram law,

w2 =u2 + v2 + 2uv cos(a)

Where,
w = magnitude of resultant velocity
u = magnitude of first velocity
v = magnitude of second velocity
a = angle between first and second velocity


2)   An object of 1 kg is attached to the string at the height of 100 m from the ground. What is the velocity of the object when it impacts on the ground, if it is released from string at 100 m?
Take acceleration due to gravity g=9.8 m/s2 (Marks: 02)

- Published on 19 Oct 15

a. 1960 m/s
b. 221.36 m/s
c. 44.27 m/s
d. none of the above
Answer  Explanation 

ANSWER: 44.27 m/s

Explanation:
No other than gravitational force is acting upon the object. Thus by using motion equation v2 = u2+ 2as and taking initial velocity of the object u = 0, we can get the final velocity that is 44.27 m/s.


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