If rain falls vertically with a velocity Vr wrt wind and wind blows with a velocity Vw from east to west, then a person standing on the roadside should hold the umbrella in the direction

1. tanθ=VwVr

2. tanθ=VrVw

3. tanθ=VrwVr2+Vw2

4. tanθ=VrVr2+Vw2

Subtopic:  Resolution of Vectors |
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The component of vector A=axi^+ayj^+azk^ along the direction of i^-j^ is

(1) ax-ay+az

(2) ax-ay

(3) (ax-ay)/2

(4) (ax+ay+az)

Subtopic:  Resolution of Vectors |
 62%
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A force is \(60^{\circ}\) 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:

1. \(25\) N 2. \(75\) N
3. \(87\) N 4. \(100\) N
Subtopic:  Resolution of Vectors |
 61%
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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[This question includes concepts from 12th syllabus]

1. 2kλr

2. kλr

3. kλ2r

4. kλ4r

Subtopic:  Electric Field |
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Electric field is given by E =100x2 . Find the potential difference between x= 10 and x= 20 m. [This question includes concepts from 12th syllabus]

1. 5 V

2. 10 V

3. 15 V

4. 20 V

Subtopic:  Relation between Field & Potential |
 65%
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The gravitational field due to a mass distribution is given by I=kx2i^, where k is a constant. Assuming the potential to be zero at infinity, find the potential at a point x = a.[This question includes concepts from Gravitation chapter]

1. ka2

2. -ka2

3. ka

4. -ka

Subtopic:  Gravitational Potential |
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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 [This question includes concepts from Work, Energy and Power chapter]

1. Pt2

2. Pt

3. Pt

4. Pt3/2

Subtopic:  Power |
 57%
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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  [This question includes concepts from Work, Energy & Power chapter]

1. 50 J

2. 40 J

3. 20 J

4. 10 J

Subtopic:  Work Energy Theorem |
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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]

1. 10 erg

2. 20 erg

3. 30 erg

4. 40 erg

Subtopic:  Concept of Work |
 76%
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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]

1. 0.6 m/s

2. 1.2 m/s

3. 1.8 m/s

4. 2.4 m/s

Subtopic:  Friction |
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