Momentum of a body moving in a straight line is p=t2+2t+1 kg m/s. Find the force acting on a body at t=2 sec

(1)  6 N

(2)  8 N

(3)  4 N

(4)  2 N

Subtopic:  Newton's Laws |
 83%
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A particle moves along straight line such that at time t its position from a fixed point O on the line is x=3t2-2. The velocity of the particle when t=2 is:

(A)  8 ms-1

(B)  4 ms-1

(C)  12 ms-1

(D)  0

Subtopic:  Differentiation |
 90%
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Coordinates of a moving particle are given by x=ct2 and y=bt2. The speed of the particle is given by

(1)  2t c+b

(2)  2t c2-b2

(3)  t c2+b2

(4)  2t c2+b2

Subtopic:  Resultant of Vectors |
 65%
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The x and y components of vector A are 4m and 6m respectively. The x, y components of vector A+B are 10m and 9m respectively. The length of B is ______ and angle that B makes with the x axis is given by _______.

(A)  0.45m, tan-11/2

(B)  4.5m, tan-11/2

(C)  45m, tan-11/2

(D)  45m, tan-11/2

Subtopic:  Resultant of Vectors |
 77%
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A particle travels with speed 50 m/s from the point (3, 7) in a direction 7i^-24j^. Find its position vector after 3 seconds.

1.  151i^+45j^

2.  45i^-137j^

3.  151i^-45j^

4.  4.5i^-151j^

Subtopic:  Resultant of Vectors |
 58%
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If \(\overrightarrow{A}={2}\hat{i}+\hat{j}\;{\&}\;\overrightarrow{B}=\hat{i}{-}\hat{j},\)  then the components of \(\overrightarrow {A}\) along with \(\overrightarrow {B}\) & perpendicular to \(\overrightarrow {B}\) respectively will be:
1. \(\frac{\hat{i} - \hat{j}}{2} ,~\frac{3}{2}\left(\hat i+\hat j\right)\)
2. \(\frac{\hat{i} - \hat{j}}{2} ,~-\frac{2}{3}\left(\hat i+\hat j\right)\)
3. \(\frac{\hat{i} - \hat{j}}{2} ,~-\frac{3}{2}\left(\hat i-\hat j\right)\)
4. \(\frac{\hat{i} - \hat{j}}{2} ,~\frac{2}{3}\left(\hat i-\hat j\right)\)

Subtopic:  Scalar Product |
 55%
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If \(\overrightarrow{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?

1. \(x\overrightarrow{a}\) is a vector in the direction of \(\overrightarrow{a}\).
2. \(x\overrightarrow{a}\) is a vector collinear to \(\overrightarrow{a}\).
3. \(x\overrightarrow{a}\) and \(\overrightarrow{a}\) have independent directions.
4. \(x\overrightarrow{a}\) is a vector perpendicular to \(\overrightarrow{a}\).
Subtopic:  Scalars & Vectors |
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If \(\theta\) is the angle between two vectors a and b, and |a×b|=a.b, then \(\theta\) is equal to:
1. \(0^\circ\)
2. \(180^\circ\)
3. \(135^\circ\)
4. \(45^\circ\)

Subtopic:  Vector Product |
 75%
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The vector \(\overrightarrow b\) which is collinear with the vector \(\overrightarrow a = \left(2, 1, -1\right)\) and satisfies the condition \(\overrightarrow a. \overrightarrow b=3\) is:
1. \(\left(1, \frac{1}{2}, \frac{-1}{2}\right)\)
2. \(\left(\frac{2}{3}, \frac{1}{3}, \frac{-1}{3}\right)\)
3. \(\left(\frac{1}{2}, \frac{1}{4}, \frac{-1}{4}\right)\)
4. \(\left(1, 1, 0\right)\)

Subtopic:  Scalar Product |
 54%
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If a, b and c are three non-zero vectors such that a+b+c=0, then the value of a.b+b.c+c.a will be:

1. Less than zero 2. equal to zero
3. greater than zero 4. 3
Subtopic:  Scalar Product |
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