Q. 1
What would be the dimensional formula for the ratio between acceleration due to gravity and gravitational constant?
• a. M2L-2
• b. M2L-1
• c. ML-2
• d. ML-1
• e. ML
• Answer: C

• Explaination: Explanation: Acceleration due to gravity at Earth is expressed as
g = GM/R2 --------------- (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/R2) ------------- (2)
Thus, dimensional formula g/G of can be found by calculating the dimensional formula for M/R2
Since, dimensional formula of M is M and R is L hence, equation 2 can be written as
(g/G) = (M/L2)
Or, (g/G) = ML-2
Thus, C is the correct answer option.
Q. 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/s2
• b. 0.32 m/s2
• c. 0.38 m/s2
• d. 0.27 m/s2
• e. 0.4 m/s2
• Answer: D

• Explaination: 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/s2
Therefore, D is the correct answer option.
Q. 3
Consider the following conclusions based on Newton’s first law.
1. Acceleration will be zero for a body obeying Newton’s first law
2. A balanced force is required to keep a body at rest or to keep it moving with uniform speed
3. An unbalanced force is required to keep a body at rest or to keep it moving with uniform speed
Based on the conclusions above, which of the following statement(s) is/are true?
• a. 1
• b. 2
• c. 3
• d. Both 1 and 2
• e. All three
• Answer: D

• Explaination: Explanation: If the net force acting on a body is zero then it means that the resultant of all the forces acting on the body is zero. Balanced forces produce zero net force acting on a body. Thus, if a body is acted upon by a balanced force, then net force acting on it is zero and hence, it will continue to retain its initial motion. Unbalanced forces have some non-zero value of force acting on a body and the body continues moving with non-uniform speed along the unbalanced force. Acceleration is time rate of change of velocity. It can also be concluded from Newton’s first law that as the velocity is uniform, change in velocity is zero and so is the acceleration of the body. Thus in view of the above discussion statements, 1 and 2 are correct and 3 is incorrect. Hence, D is the correct answer option.
Q. 4
Consider the figure given below. A block of wood of mass 10 kg is kept on a rough surface. Which of the following statements is true in respect of the frictional force that will develop such that the block moves in the direction of a force of 100 N as shown in the figure below? • a. Frictional force
• b.
• c.
• d.
• e.
• Answer: A