Home
Class 12
MATHS
Forces of magnitudes 5 and 3 units acti...

Forces of magnitudes 5 and 3 units acting in the directions ` 6hati + 2hatj + 3hatk and 3 hati - hati +6hatk` respectively act on a particle which is displaced from the point ( 2,2,-1) to ( 4,3,1) . The work done by the forces, is

A

148 unit

B

` 148/7` unit

C

296 units

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` vecF` be the resultant force and `vecd` be the displacement vector. Then,
` vecF=5 ((6hati +2hatj +3hatk))/ (sqrt(36+4+9))+3 ((3hati -2hatj +6hatk)) /(sqrt(9 +4+ 36)) = 1/7 (39 hati + 4hatj +33 hatk)`
` and vecd = (4hati + 3hatj +hatk) - (2hati +2hatj -hatk) = 2hati +hatj + 2hatk`
Total work done = ` vecF. vecd`
`Rightarrow ` Total work done = ` 1/7 (39 hati +4hatj +33hatk).(2hati +hatj +2hatk) `
Total work done ` = 1/7 ( 78 +4 +66) = 148/7` units.
Promotional Banner

Topper's Solved these Questions

  • SCALER AND VECTOR PRODUCTS OF TWO VECTORS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|12 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA|Exercise Exercise|65 Videos

  • SOLUTIONS OF TRIANGLES

    OBJECTIVE RD SHARMA|Exercise Exercise|20 Videos

Similar Questions

Explore conceptually related problems

Force of magnitudes 3 and 4 units acting along 6 hati + 2hat j + 3hatk and 3hatj-2hatj+6hatk respectively act on a particle and displace it from (2,2,-1) to (4,3,1) . The work done is

If the constant forces 2hati-5hatj+6hatk and -hati+2hatj-hatk act on a particle due to which it is displaced from a point A (4,-3,-2) to a point B (6,1,-3), then the work done by the forces is

Two forces whose magnitudes are 2N and 3N act on a particle in the direction of the vectros 2hati+4hatj+4hatk and 4hati-4hatj+2hatk respectively. If the particle is displaced from the origin O to the point (1,2,2). Find the work done.

The unit vector perpendicular to the vectors 6hati+2hatj+3hatk and 3hati-6hatj-2hatk , is

Two forces hati+hatj+hatk N and hati+2hatj+3hatk N act on a particle and displace it from (2,3,4) to point (5,4,3). Displacement is in m. work done is

A particle is acted upon by constant forces 4hati +hatj - 3hatk and 3hati + hatj -hatk which displace it from a point hati + 2hatj + 3hatk to the point 5hati + 4hatj + hatk . The work done in standard units by the forces is given by: