Vector $\stackrel{\to }{\mathrm{A}}$ is of length 2 cm and is 60$°$ above the x-axis in the first quadrant. Vector $\stackrel{\to }{\mathrm{B}}$ is of length 2 cm and 60$°$ below the x-axis in the fourth quadrant. The sum $\stackrel{\to }{\mathrm{A}}$+$\stackrel{\to }{\mathrm{B}}$ 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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Difficulty Level:

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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Difficulty Level:

Temperature of a body varies with time as , where ${\mathrm{T}}_{0}$ is the temperature in Kelvin at , then the rate of change of temperature $\left(\frac{\mathrm{dT}}{\mathrm{dt}}\right)$ at  is-

1.

2.

3.

4.

Concept Questions :-

Differentiation
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Difficulty Level:

If the distance 's' travelled by a body in time 't' is given by $\mathrm{s}=\frac{\mathrm{a}}{\mathrm{t}}+{\mathrm{bt}}^{2}$ then the acceleration equals

(A)  $\frac{2\mathrm{a}}{{\mathrm{t}}^{3}}+2\mathrm{b}$

(B)  $\frac{2\mathrm{s}}{{\mathrm{t}}^{3}}$

(C)  $2\mathrm{b}-\frac{2\mathrm{a}}{{\mathrm{t}}^{3}}$

(D)  $\frac{\mathrm{s}}{{\mathrm{t}}^{2}}$

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Difficulty Level:

The velocity of a particle moving on the x-axis is given by $\mathrm{v}={\mathrm{x}}^{2}+\mathrm{x}$ where v is in m/s and x is in m. Find its acceleration in $\mathrm{m}/{\mathrm{s}}^{2}$ when passing through the point x=2m.

1.  0

2.  5

3.  11

4.  30

Concept Questions :-

Integration
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Difficulty Level:

A particle moves in the XY plane and at time t is at the point whose coordinates are . 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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Difficulty Level:

A particle moves in the x-y plane with velocity ${\mathrm{v}}_{\mathrm{x}}=8\mathrm{t}-2$ and ${\mathrm{v}}_{\mathrm{y}}=2$. If it passes through the point x=14 and y=4 at t=2 sec. The equation of the path is

(A)  $\mathrm{x}={\mathrm{y}}^{2}-\mathrm{y}+2$

(B)  $\mathrm{x}=\mathrm{y}+2$

(C)  $\mathrm{x}={\mathrm{y}}^{2}+2$

(D)  $\mathrm{x}={\mathrm{y}}^{2}+\mathrm{y}+2$

Concept Questions :-

Integration
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Difficulty Level:

A motor boat of mass m moving along a lake with velocity ${\mathrm{V}}_{0}$. 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?

(A)  ${\mathrm{mV}}_{0}/\mathrm{r}$

(B)

(C)  ${\mathrm{mV}}_{0}/2\mathrm{r}$

(D)  $2{\mathrm{mV}}_{0}/\mathrm{r}$

Concept Questions :-

Integration

Difficulty Level:

A particle is moving along positive x-axis. Its position varies as $\mathrm{x}={\mathrm{t}}^{3}-3{\mathrm{t}}^{2}+12\mathrm{t}+20$, where x is in meters and t is in seconds.

Initial velocity of the particle is

(A)  1 m/s

(B)  3 m/s

(C)  12 m/s

(D)  20 m/s

Concept Questions :-

Differentiation
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Difficulty Level:

A particle is moving along positive x-axis. Its position varies as $\mathrm{x}={\mathrm{t}}^{3}-3{\mathrm{t}}^{2}+12\mathrm{t}+20$, where x is in meters and t is in seconds.

Initial acceleration of the particle is

(A)  Zero

(B)

(C)

(D)

Concept Questions :-

Differentiation