Home
Class 12
PHYSICS
The resultant of two forces is 20/3 N. I...

The resultant of two forces is 20/3 N. If one of the force is 20 N and makes an angle of 30° with the resultant, the other force has a mangitude:

A

10 N

B

`20sqrt3 N`

C

`10sqrt3N`

D

`20 N`

Text Solution

Verified by Experts

The correct Answer is:
d
Let theta the angle between two forces `vecF_(1)`, and `vecF_(2)`Now sum of components of individual forces must be equal to component of resultant force along X-axis
:.` Fcos 30^(@) = F_(1) +F_(2) cos theta`

`implies20sqrt3xx(sqrt3)/(2)=20+F_(2)costheta=10`
`impliesF_(2)costheta=10...(i)`
Along y-direction`Fsin30^(@)=F_(1)cos90^(@)+F_(2)sintheta`
`20sqrt3xx(1)/(2)=0+F_(2)sintheta`
`impliesF_(2)sintheta=10sqrt3...(ii)`
Squaring and adding (i) and (ii)
`F_(2)^(2)(cos^(2)theta+sin^(2)theta)=100+300`
`F_(2)=20N`
Hence correct choice is (d).
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LAWS OF MOTION

    MODERN PUBLICATION|Exercise MULTIPLE CHOICE QUESTION (LEVEL-II)|64 Videos

  • LAWS OF MOTION

    MODERN PUBLICATION|Exercise MULTIPLE CHOICE QUESTION (LEVEL-III)|2 Videos

  • HEAT AND THERMODYNAMICS

    MODERN PUBLICATION|Exercise Recent Competitve Questions|17 Videos

  • MAGNETOSTATICS

    MODERN PUBLICATION|Exercise RECENT COMPETITIVE QUESTION|5 Videos

Similar Questions

Explore conceptually related problems

Define resultant force.

The greatest and least resultant of two forces acting at a point are 29N and 5N. If each force is increased by 3N, find the magnitude of the resultant of the two new forces when they act at right angles to each other.

Knowledge Check

  • The resultant of two forces is 20 N when one of force is 20 sqrt(3) N and angle between two forces is 30° then what is value of second force ?

    A
    10N
    B
    20N
    C
    `20sqrt(3)N`
    D
    `10sqrt(3)N`

  • A force of 50 N moves a body

    A
    Frictional force exerted on the body is less than 50N
    B
    Frictional force exerted on the body is more than 50 N
    C
    None of these
    D
    Both a and b

  • The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is

    A
    `90^(@)`
    B
    `180^(@)`
    C
    `60^(@)`
    D
    `120^(@)`

    • Similar Questions

    Explore conceptually related problems

    If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.

    The sum of the magnitudes of two forces acting at a point is 16 N. The resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N. If the smaller force is magnitude x, then the value of x is

    The resultant of two forces acting at an angle of 120° is 10 kg wt and is perpendicular to one of the forces. That force is :

    The resultant of two forces acting an angle of 120^(@) is 10 kg wt and is perpendicular to one of the forces .That force is

    The resultant of two forces, one double than the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is :

    Home
    Profile