Sample paper 4
Question 1
Which of the following is a dimensionally correct representation for angular momentum?
A. M
2
L
2
T
-1
B. M
2
L
1
T
-1
C. M
2
L
1
T
-2
D. ML
2
T
-1
E. ML
1
T
-1
Correct Answer: D
Explanation:
Angular momentum is given as
L = Iω ------------ (1)
SI unit for I is kgm
2
. Hence, dimensional formula of I becomes ML
2
. Angular velocity is given as
ω = v/ r
SI unit of v is m/s and that of r is m. Hence, SI unit of angular velocity becomes
(m/s)/m Or 1/s
Therefore, dimensional formula of angular velocity is T
-1
. Thus, dimensional formula of angular
momentum from equation 1 becomes
ML
2
/ T Or ML
2
T
-1
Hence, D is the correct answer option.
Question 2
A train at rest starts from station A and travels to station B at a distance of 2 km in 4 minutes?
Consider the following statements.
Instantaneous speed of the train is 8.33 m/s
Average speed of the train is 8.33 m/s
Instantaneous acceleration of the train is 8.33 m/s
2
A.
Which of the following statement(s) is/are true?
B. 1
C. 2
D. 3
E. Both 1 and 3
F. Both 2 and 3
Correct Answer: B
Explanation:
Instantaneous speed of a body is the speed possessed by it at any particular time instant.
Instantaneous speed is a variable and changes accordingly. Speedometer is a device that is used by
the vehicles to know the speed possessed by it at that instant. Average velocity or speed provides
speed of the body for the full journey. It is given as the total distance travelled in total time taken. As in
the question the total time and the total distance are given, hence average speed can be found as
Average speed = Total Distance / Total Time ------------- (1)
