Chapter Chosen

Motion in Straight Line

Book Chosen

Physics Part I

Subject Chosen

Physics

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation straight s equals 1 third straight t squared, where t is in s. Work done by the force in 2 s is:

  • 5 over 19 straight J
  • 3 over 8 straight J
  • 8 over 3 straight J
  • 19 over 5 straight J

C.

8 over 3 straight J

If a constant force is applied on the object causing a displacement in it, then it is said that work has been done on the body to displace it.
  Work done by the force  = Force x Displacement
or          W = F x s                            ...(i)
But from Newton's 2nd law, we have
  Force  =  Mass x Acceleration
i.e.,       F = ma                                ...(ii)
Hence, from Eqs. (i) and (ii), we get
straight W space equals space mas space equals space straight m open parentheses fraction numerator straight d squared straight s over denominator dt squared end fraction close parentheses straight s space space space space space space... left parenthesis iii right parenthesis space space space open parentheses because space straight a space equals space fraction numerator straight d squared straight s over denominator dt squared end fraction close parentheses
Now comma space we space have comma space space straight s space equals space 1 third straight t squared
therefore space space space space space space space space space fraction numerator straight d squared straight s over denominator dt squared end fraction space equals space straight d over dt open square brackets straight d over dt open parentheses 1 third straight t squared close parentheses close square brackets
space space space space space space space space space space space space space space space space space space space equals straight d over dt cross times open parentheses 2 over 3 straight t close parentheses
space space space space space space space space space space space space space space space space space space equals 2 over 3 dt over dt space space space space space space
space space space space space space space space space space space space space space space space space space equals 2 over 3 space space space space space space space
space space space space space space space space space space space space space space space
Hence, Eq (ii) becomes
                straight W space equals 2 over 3 ms space equals space 2 over 3 straight m cross times 1 third straight t squared
                   equals 2 over 9 mt squared
We have given
                   straight m equals 3 space kg comma space straight t space equals space 2 straight s
therefore space space space space straight w space equals space 2 over 9 cross times 3 cross times left parenthesis 2 right parenthesis squared space equals space 8 over 3 straight J
 

If a constant force is applied on the object causing a displacement in it, then it is said that work has been done on the body to displace it.
  Work done by the force  = Force x Displacement
or          W = F x s                            ...(i)
But from Newton's 2nd law, we have
  Force  =  Mass x Acceleration
i.e.,       F = ma                                ...(ii)
Hence, from Eqs. (i) and (ii), we get
straight W space equals space mas space equals space straight m open parentheses fraction numerator straight d squared straight s over denominator dt squared end fraction close parentheses straight s space space space space space space... left parenthesis iii right parenthesis space space space open parentheses because space straight a space equals space fraction numerator straight d squared straight s over denominator dt squared end fraction close parentheses
Now comma space we space have comma space space straight s space equals space 1 third straight t squared
therefore space space space space space space space space space fraction numerator straight d squared straight s over denominator dt squared end fraction space equals space straight d over dt open square brackets straight d over dt open parentheses 1 third straight t squared close parentheses close square brackets
space space space space space space space space space space space space space space space space space space space equals straight d over dt cross times open parentheses 2 over 3 straight t close parentheses
space space space space space space space space space space space space space space space space space space equals 2 over 3 dt over dt space space space space space space
space space space space space space space space space space space space space space space space space space equals 2 over 3 space space space space space space space
space space space space space space space space space space space space space space space
Hence, Eq (ii) becomes
                straight W space equals 2 over 3 ms space equals space 2 over 3 straight m cross times 1 third straight t squared
                   equals 2 over 9 mt squared
We have given
                   straight m equals 3 space kg comma space straight t space equals space 2 straight s
therefore space space space space straight w space equals space 2 over 9 cross times 3 cross times left parenthesis 2 right parenthesis squared space equals space 8 over 3 straight J
 

737 Views

Is absolute rest or absolute motion possible?

Absolute rest and absolute motion is not possible because there is no point in the universe which is at rest and can be taken as point of reference. The planet Earth is in continuous motion. 
1986 Views

What is the most essential thing to study the motion of a body?

The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion. 
650 Views

Can a body be always at rest in some frame?

Yes, a body is always at rest in a frame which is fixed with the body itself. 
746 Views

What is rest?

When an object does not change its position with time, with respect to it's surroundings. In such a case the object is said to be at rest. 
1215 Views

What is motion?

When an object changes it's position with time, with respect to it's surroundings, the object is said to be in motion. 
657 Views