Sample paper 5
Question 1
What would be the dimensional formula for the ratio between acceleration due to gravity and
gravitational constant?
A. M
2
L
-2
B. M
2
L
-1
C. ML
-2
D. ML
-1
E. ML
Correct Answer: C
Explanation:
Acceleration due to gravity at Earth is expressed as
g = GM / R
2
------------- (1)
Since we have to find the dimensional formula for the ratio between g and G, equation 1 can be
written as
g / G = M / R
2
------------- (2)
Thus, dimensional formula of g/G can be found by calculating the dimensional formula for M / R
2
.
Since, dimensional formula of M is M and R is L hence, equation 2 can be written as
g / G = M / L
2
Or g / G = ML
-2
Thus, C is the correct answer option.
Question 2
A car speeds up from 15 m/s to 27 m/s in 45 s. What would be the acceleration of the car?
A. 0.15 m/s
2
B. 0.32 m/s
2
C. 0.38 m/s
2
D. 0.27 m/s
2
E. 0.4 m/s
2
Correct Answer: D
Explanation:
Here the initial speed, the final speed and the time taken are given and so we can use the kinematic
equation
v = u + at ------------- (1)
Putting these values in equation 1 we get
27 = 15 + a * 45
Or a = 0.27 m/s
2
Therefore, D is the correct answer option.