Q. 1
Force acting on an object is given as F = Xx^{1}
(Where x is the distance by which the body is displaced due to the applied force)
What would be the dimensional formula for X?
(Where x is the distance by which the body is displaced due to the applied force)
What would be the dimensional formula for X?
 a. MLT^{2}
 b. MLT^{1}
 c. M^{1}LT^{1}
 d. M^{1}L^{2}T^{1}
 e. ML^{2}T^{2}
 Answer: E

Explaination: Explanation: From dimensional analysis we know that dimensional formula of the left hand side of an expression should be the same be the same as the dimensional formula of the individual quantities on the right hand side. Force has the SL unit of. Therefore, the dimensional formula of force becomes. Dimensional formula of is L. Hence, dimensional formula of becomes. As said earlier, should have the same dimensional formula as F. Therefore, it can be written as
MLT^{2} = X * L^{1}
X = ML^{2}T^{2}
Therefore, E is the correct answer option.
Q. 2
Consider the figure and the statements given below. ( v is velocity and t is time)
1. The graph is for a body that is accelerating
2. The graph is for a body that is falling freely
3. The graph is for a body that has constant velocity
Which of the following statement(s) is true in accordance to the given figure?
1. The graph is for a body that is accelerating
2. The graph is for a body that is falling freely
3. The graph is for a body that has constant velocity
Which of the following statement(s) is true in accordance to the given figure?
 a. 2
 b. 1
 c. 3
 d. Both 1 and 2
 e. Both 2 and 3
 Answer: A
 Explaination: Explanation: The graph given in the question is between velocity and time. Slope of the velocity time graph is linear here. Therefore, velocity increase with each instant but change in velocity per unit time is constant throughout the travel. Thus, 3 is an incorrect statement and so is option C. Acceleration of a body is defined as the rate of change of velocity per unit time. As said earlier, for a linear slope between velocity and time, change in velocity is constant per unit time and thus, acceleration is constant for the entire travel. Therefore, statement 1 is incorrect and so is option B. A body falls freely under gravity only. A free failing body always experiences uniform acceleration throughout the travel. Thus, we can say that acceleration is constant for a free fall and the graph essentially represents the motion of free fall. Thus, statement 2 is correct and so A is the correct answer option. In view of the above discussion, options D and E are incorrect as well.
Q. 3
If a block of wood weighs 1000 N, What would be its mass?
 a. 102.04 kg
 b. 10.24 kg
 c. 1020.44 kg
 d. 1.24 kg
 e. 110.24 kg
 Answer: A

Explaination: Explanation: Weight of a body is given as
W = mg (1)
Putting the value of W and g in equation 1 we get
1000 = m * 9.8
m = 102.04 kg
Therefore, A is the correct answer option.
Q. 4
A force of 25 N is acting along the North direction and a force of 12 N is acting along the South direction on a body of mass 1.5 kg. What acceleration will the force bring in the body?
 a. 9.87 m/s^{2}
 b. 2.36 m/s^{2}
 c. 4.67 m/s^{2}
 d. 7.67 m/s^{2}
 e. 8.67 m/s^{2}
 Answer: E

Explaination: Explanation: A body undergoes acceleration due to an unbalanced force. The unbalanced force here is given as
F = 25 ??? 12 Or F = 13 N
According to Newton???s second law of motion
F = ma (1)
13 = 1.5 * a
a = 8.67 m/s^{2}
Therefore, E is the correct answer option.
Q. 5
If a wheel is rotating with an angular velocity of 2.5 rad/s, what is the time taken by the wheel to complete one full rotation?
 a. 1.57 s
 b. 2.51 s
 c. 1.84 s
 d. 3.52 s
 e. 2.22 s
 Answer: B

Explaination: Explanation: Time taken to complete one rotation is known as time period. Angular velocity is related to time period as
?? = 2?? / T (1)
Putting the values of (?? = 3.14) and ?? in equation 1 we get
2.5 = (2 * 3.14) / T
T = 2.51 s
Therefore, B is the correct answer option.
Q. 6
An object is to be lifted from the ground to a height of 5m in 25 seconds. If the energy consumed during the process is 2000 J, what is the power required?
 a. 75 J/s
 b. 72 J/s
 c. 80 J/s
 d. 100 J/s
 e. 125 J/s
 Answer: C

Explaination: Explanation: Power is given as
P = W / t (1)
Putting the values in equation 1 we get
P = 2000 / 25
P = 80 J / s or watt
Hence, C is the correct answer option.
Q. 7
A block of mass M, connected to a spring of spring constant k ( a springmass system ), is executing SHM with time period, T on Earth. If the same system executes SHM on the surface of Moon, what will be the new time period?
 a. More than that on the Earth
 b. Less than that on the Earth
 c. Same as that on the Earth
 d. Zero
 e. Not enough data is provided to predict the answer
 Answer: C

Explaination: Explanation: Time period is given as
T = 2 ?? ???(M/k) (1)
At the surface of the Moon, acceleration due to gravity is (1/6)th of that on the surface of the Earth. As, there is no term related to acceleration due to gravity in equation 1, time period of the system will remain unaffected. Hence, time period of the system on the moon will be the same as that of the system on the Earth. Therefore, C is the correct answer option.
Q. 8
If the speeds of sound in solid, liquid and gas are arranged in increasing order, which of the following is a correct arrangement?
 a. Solids
 b.
 c.
 d.
 e.
 Answer: A