The scalar product of two vectors is 8 and the magnitude of vector product is 83. The angle between them is:

(A)  30°

(B)  60°

(C)  120°

(D)  150°

Concept Questions :-

Vector Product
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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°

Concept Questions :-

Resultant of Vectors
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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

Concept Questions :-

Resultant of Vectors
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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

(A)  0 N

(B)  9.81 N

(C)  2×9.81 N

(D)  3×9.81 N

Concept Questions :-

Resultant of Vectors
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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=-4K, then the rate of change of temperature dTdt at t=π sec is-

1.  8 K

2.  80 K

3.  8 K/sec

4.  80 K/sec

Concept Questions :-

Differentiation
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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

(A)  2at3+2b

(B)  2st3

(C)  2b-2at3

(D)  st2

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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

Concept Questions :-

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?

(A)  1/3 sec

(B)  2/3 sec

(C)  3/2 sec

(D)  never

Concept Questions :-

Differentiation
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A particle moves in the x-y plane with velocity vx=8t-2 and vy=2. If it passes through the point x=14 and y=4 at t=2 sec. The equation of the path is

(A)  x=y2-y+2

(B)  x=y+2

(C)  x=y2+2

(D)  x=y2+y+2

Concept Questions :-

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A motor boat of mass m moving along a lake with velocity V0. At t=0, the engine of the boat is shut down. Magnitude of resistance force offered to the boat is equal to rV. (V is instantaneous speed). What is the total distance covered till it stops completely? Hint: Fx=mVdVdx=-rV

(A)  mV0/r

(B)  3 mV0/2r

(C)  mV0/2r

(D)  2mV0/r

Concept Questions :-

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