What is the torque of a force F=2i^-3j^+4k^ newton acting at a point r=3i^+2j^+3k^  metre about the origin? (Given: τ =r ×F)

1. 6i^-6j^+12k^ 

2. 17i^-6j^-13k^ 

3. -6i^+6j^-12k^ 

4. -17i^+6j^-13k^ 

Subtopic:  Vector Product |
 69%
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Three non zero vectors A, B & C satisfy the relation A·B=0 & A·C=0. Then A can be parallel to:

(1)  B

(2)  C

(3)  B·C

(4)  B×C

Subtopic:  Scalar Product |
 68%
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The scalar product of two vectors is 8 and the magnitude of vector product is 83. The angle between them is:

(1)  30°

(2)  60°

(3)  120°

(4)  150°

Subtopic:  Vector Product |
 73%
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Given: a+b+c=0. Out of the three vectors a, b and c two are equal in magnitude. The magnitude of the third vector is 2 times that of either of the two having equal magnitude. The angles between the vectors are:

(A)  90°, 135°, 135°

(B)  30°, 60°, 90°

(C)  45°, 45°, 90°

(D)  45°, 60°, 90°

Subtopic:  Resultant of Vectors |
 56%
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Vector A is of length 2 cm and is 60° above the x-axis in the first quadrant. Vector B is of length 2 cm and 60° below the x-axis in the fourth quadrant. The sum A+B is a vector of magnitude -

(A)  2 along + y-axis

(B)  2 along + x-axis

(C)  1 along - x-axis

(D)  2 along - x-axis

Subtopic:  Resultant of Vectors |
 81%
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Six forces, 9.81 N each, acting at a point are coplanar. If the angle between neighboring forces are equal, then the resultant is

(1)  0 N

(2)  9.81 N

(3)  2×9.81 N

(4)  3×9.81 N

Subtopic:  Resultant of Vectors |
 81%
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Temperature of a body varies with time as T=T0+at2+b sintK, where T0 is the temperature in Kelvin at t=0 sec & a=2/π K/s2 & b=-K, then the rate of change of temperature dTdt at t=π sec is:
1. \(8~\text{K}\)
2. \(80~\text{K}\)
3. \(8~\text{K/sec}\)
4. \(80~\text{K/sec}\)

Subtopic:  Differentiation |
 57%
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If the distance 's' travelled by a body in time 't' is given by s=at+bt2 then the acceleration equals

(1)  2at3+2b

(2)  2st3

(3)  2b-2at3

(4)  st2

Subtopic:  Differentiation |
 74%
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The velocity of a particle moving on the x-axis is given by v=x2+x where v is in m/s and x is in m. Find its acceleration in m/s2 when passing through the point x=2m.

1.  0

2.  5

3.  11

4.  30

Subtopic:  Differentiation |
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A particle moves in the XY plane and at time t is at the point whose coordinates are t2, t3-2t. Then at what instant of time, will its velocity and acceleration vectors be perpendicular to each other?

(1)  1/3 sec

(2)  2/3 sec

(3)  3/2 sec

(4)  never

Subtopic:  Scalar Product |
 62%
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