Mathematics In Physics Test

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Mathematics In Physics Test - 12

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Question 1
1 / -0

The 9 kg block is moving to the right with a velocity of 0.6 m/s on a horizontal surface when a force F, whose time variation is shown in the graph, is applied to it at time t = 0. Calculate the velocity v of the block when t= 0.4s. The coefficient of kinetic fricton is μk = 0.3. [This question includes concepts from Work, Energy & Power chapter]

A
0.6 m/s

B
1.2 m/s

C
1.8 m/s

D
2.4 m/s

Solution

Change in the momentum of the body over 0.4 seconds :
Question 2
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The relationship between force and position is shown in the figure given (in one dimensional case). Find the work done by the force in displaying a body from x= 1 cm to x= 5cm is [This question includes concepts from Work, Energy and Power chapter]

A
10 erg

B
20 erg

C
30 erg

D
40 erg

Solution

Work done= covered area on force-displacement graph

= 1 X 10 + 1 X 20 - 1 X 20 + 1 X 10 =20 erg.
Question 3
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The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and initial velocity is 2 m/s. When the distance covered by the body is 4 m, its kinetic energy would be

A
50 J

B
40 J

C
20 J

D
10 J

Solution

Initial kinetic energy of the body

Final kinetic energy= Initial energy - work done against resistive force (Area between graph and displacement axis)

If kinetic energy of the body increases, work is positive i.e. body moves in the direction of the force (or field) and if kinetic energy decreases work will negative and object will move opposite to the force (or field).
Question 4
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A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as

A
P ∝ t²

B
P ∝ t

C
P ∝ √t

D
P ∝ t^3/2

Solution
Question 5
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The gravitational field due to a mass distribution is given by where k is a constant. Assuming the potential to be zero at infinity, find the potential at a point x = a.

A
k/a²

B
−k/a²

C
k/a

D
−k/a

Solution
Question 6
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Electric field is given by E = 100/x² . Find the potential difference between x= 10 and x= 20 m.

A
5 V

B
10 V

C
15 V

D
20 V

Solution
Question 7
1 / -0

Calculate the electric field on the axis of a very long uniformly charged, thin rod at a distance r from one end. The charge per unit length of the rod is λ.

A
2kλ / r

B
kλ / r

C
kλ / 2r

D
kλ / 4r

Solution

Field at point P due to any section of the rod will be directed leftward.

Consider a very small section of length dx at a distance x from P. The charge on this section is dq such that dq= λdx. The electric field at P due to this section is
Question 8
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If rain falls vertically with a velocity V_r wrt wind and wind blows with a velocity V_w from east to west, then a person standing on the roadside should hold the umbrella in the direction

A

B

C

D

Solution

Man should hold the umbrella in the direction of the relative velocity of the rain wrt man. If V_r → velocity of rain wrt wind,

V_w → velocity of wind and V_r,g → relative velocity of rain w.r.t ground
Question 9
1 / -0

A

B

C

D

Solution

Hint: Use the scalar product of vectors.

Step 1: Draw a diagram
Question 10
1 / -0

A force is 60 ° inclined to the horizontal. If its rectangular component in the horizontal direction is 50 N, then the magnitude of the force in the vertical direction is

A
25 N

B
75 N

C
87 N

D
100 N

Solution