Explanation:
Resultant force is given as
R = √( F
1
2
+ F
2
2
+ 2F
1
F
2
cos θ) ------------ (1)
As both the forces are acting orthogonally, θ = 90
o
. Modifying equation 1 we get
R = √( F
1
2
+ F
2
2
+ 2F
1
F
2
cos 90
o
)
Or R = √( F
1
2
+ F
2
2
) ------------- (2)
If we take F
1
= 6 N and F
2
= 8 N and putting the values in equation 2 we get
R = 10N
Putting the values as mentioned in options A, C, D and E, we get the value of the resultant force as
6.4 N, 9.43 N, 11.3 N and 7.07 N.
Thus, for only one combination i.e. 6 N and 8 N we have a resultant force of 10 N.
Hence, B is the correct answer option.
Question 5
If a ferry-wheel completes 100 rotations in 15 s, with what velocity is it rotating?
A. 41.87 rad/s
B. 42.34 rad/s
C. 40.56 rad/s
D. 45.45 rad/s
E. 6.67 rad/s
Correct Answer: A
Explanation:
Velocity with which the ferry-wheel is rotating is its angular velocity. It is given as
ω = [(N * 2π)/ t] ----------------- (1)
Putting the values in equation 1 we get
ω = [(100 * 2π)/ 15] (π = 3.14)
ω = 41.87 rad/s
Therefore, A is the correct answer option.
Question 6
A 5 kg block of ice, kept at some height, has the potential energy of 1000 Joules. What is the
height at which the block has been kept?
A. 20.4 m
B. 21.2 m
C. 10.5 m
D. 11.4 m
E. 24.3 m
Correct Answer: A
Explanation:
Potential energy is given as
PE = mgh ---------------- (1)
Putting the values in equation 1 we get
1000 = 5 * 9.8 * h
