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Standard XII

Physics

Order of Magnitude

Constant forc...

Question

Constant forces $P = 2 i - 5 j + 6 k$ and $Q = - i + 2 j - k$ act on a particle is displaced from a point A with position vector $4 i - 3 j - 2 k$ to point B with position vector $6 i + j - 3 k .$ Calculate work done for this process is

-19 units

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-15 units

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15 units

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19 units

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Solution

The correct option is B -15 units
If R is the resultant of two forces P and Q then $R = P + Q = i - 3 j + 5 k .$
Also the displacement of the particle.
$= \to A B = (6 i + j - 3 k) - (4 i - 3 j - 2 k) = 2 i + 4 j - k .$
Hence required work done
$= R . \to A B = (i - 3 j + 5 k) . (2 i + 4 j - k)$ $= 2 - 12 - 5 = - 15.$

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Similar questions

A line passing through the point A with position vector a= 4i+ 2j+2k is parallel to the vector b = 2i+3j+6k . Find the length of the perpendicular drawn on this line from a point P with position vector r= i + 2 j+ 3k

Q. The distance of the point

B

with position vector

i + 2 j + 3 k

from the line passing through the point

A

with position vector

4 i + 2 j + 2 k

and parallel to the vector

2 i + 3 j + 6 k

Q. Forces acting on a particle have magnitudes of

5, 3

and

1

units and act in the direction of the vectors

6 i + 2 j + 3 k, 3 i - 2 j + 6 k

and

2 i - 3 j - 6 k,

respectively. They remain constant while the particle is displaced from the point

A (2, - 1, - 3)

B (5, - 1, 1)

. The work done is equal to

Q. Three force

\to P, \to Q

and

\to R

, each of

15

units, act along

A B, B C

and

C A

respectively. The position vectors of

A, B

and

C

are

\to O A = \to 2 i - \to j + \to 3 k

\to O B = \to 5 i + \to 3 j - \to 2 k

and

\to O C = - \to 2 i + \to 2 j + \to 3 k

respectively. The resultant force vector is

Q. Forces acting on a particle have magnitudes

5, 3, 1 k g . w t

and act in the directions of the vectors

6 i + 2 j + 3 k, 3 i - 2 j + 6 k

and

2 i - 3 j - 6 k

respectively.These remain constant while the particle is displaced from A (4, -2, -6) to B (7,-2,-2). Find the work done.

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Constant forces P=2i−5j+6k and Q=−i+2j−k act on a particle is displaced from a point A with position vector 4i−3j−2k to point B with position vector 6i+j−3k. Calculate work done for this process is

The correct option is B -15 unitsIf R is the resultant of two forces P and Q then R=P+Q=i−3j+5k.Also the displacement of the particle.=→AB=(6i+j−3k)−(4i−3j−2k)=2i+4j−k.Hence required work done=R.→AB=(i−3j+5k).(2i+4j−k) =2−12−5=−15.

Constant forces $P = 2 i - 5 j + 6 k$ and $Q = - i + 2 j - k$ act on a particle is displaced from a point A with position vector $4 i - 3 j - 2 k$ to point B with position vector $6 i + j - 3 k .$ Calculate work done for this process is