Two constant forces  and  act on a body and displace it from the position  to the position . What is the work done?

(A)  9 Joule

(B)  41 Joule

(C)  -3 Joule

(D)  None of these

Concept Questions :-

Scalar Product
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The two vectors $\mathrm{A}=2\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}+3\stackrel{^}{\mathrm{k}}$ and $\mathrm{B}=7\stackrel{^}{\mathrm{i}}-5\stackrel{^}{\mathrm{j}}-3\stackrel{^}{\mathrm{k}}$ are -

1.  parallel

2.  perpendicular

3.  anti-parallel

4.  None of these

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Two vectors $\mathrm{P}=2\stackrel{^}{\mathrm{i}}+\mathrm{b}\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$ and $\mathrm{Q}=\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}$ will be perpendicular if -

(A)  b=0

(B)  b=1

(C)  b=2

(D)  b=-4

Concept Questions :-

Scalar Product
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A vector perpendicular to $\left(4\stackrel{^}{\mathrm{i}}-3\stackrel{^}{\mathrm{j}}\right)$ is -

(A)  $4\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}$

(B)  $7\stackrel{^}{\mathrm{k}}$

(C)  $6\stackrel{^}{\mathrm{i}}$

(D)  $3\stackrel{^}{\mathrm{i}}-4\stackrel{^}{\mathrm{j}}$

Concept Questions :-

Scalar Product
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Angle that the vector $\mathrm{A}=2\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}$ makes with y-axis is -

(A)

(B)

(C)

(D)

Concept Questions :-

Scalar Product
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A vector A points, vertically upward and, B points towards north. The vector product $\mathrm{A}×\mathrm{B}$ is -

1.  along west

2.  along east

3.  zero

4.  vertically downward

Concept Questions :-

Vector Product
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The linear velocity of a rotating body is given by $\mathrm{v}=\mathrm{\omega }×\mathrm{r}$, where $\mathrm{\omega }$ is the angular velocity and r is the radius vector. The angular velocity of a body $\mathrm{\omega }=\stackrel{^}{\mathrm{i}}-2\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$ and their radius vector  is -

(A)

(B)

(C)

(D)

Concept Questions :-

Vector Product
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The displacement x of a particle along a straight line at time t is given by $\mathrm{x}={\mathrm{a}}_{0}+{\mathrm{a}}_{1}\mathrm{t}+{\mathrm{a}}_{2}{\mathrm{t}}^{2}$. The acceleration of the particle is

(A)  ${\mathrm{a}}_{0}$

(B)  ${\mathrm{a}}_{1}$

(C)  $2{\mathrm{a}}_{2}$

(D)  ${\mathrm{a}}_{2}$

Concept Questions :-

Differentiation
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The displacement of a particle is given by $\mathrm{y}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^{2}-{\mathrm{dt}}^{4}$. The initial velocity and acceleration are respectively

(A)  b, -4d

(B)  -d, 2c

(C)  b, 2c

(D)  2c, -4d

Concept Questions :-

Differentiation
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The momentum is given by p=4t+1, the force at t=2s is

(A)  4 N

(B)  8 N

(C)  10 N

(D)  15 N

Concept Questions :-

Differentiation
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Difficulty Level: