Answer
Verified
397.5k+ views
Hint: When the man moves forward he applies a normal force on the trolley which makes it move backward. Some of the momentum from his foot gets transferred to the trolley. Hence we can use the conservation of momentum to calculate their final velocity.
Complete solution:
In the above case the man moves with some velocity and hence has some momentum. This momentum gets transferred to the trolley due the normal produced by the trolley due to a backward force by the foot.
Using law of conservation of momentum,
The forward momentum of the man = backward motion of the man and the trolley moving together.
Since momentum of an object is given by the product of mass times the velocity, i.e. mathematically given by p= mv $kgm{{s}^{-1}}$.
Mathematically we can represent the above condition as,
${{P}_{FORWARD}}={{P}_{BACKWARD}}$
Mass of the man is $80kg$ and moves with velocity of $1m{{s}^{-1}}$
Mass of man + Mass of trolley=$320+80=400kg$
Substituting in the above equation conservation of momentum,
${{P}_{FORWARD}}={{P}_{BACKWARD}}$
$80\times 1=400\times v$ where v is the velocity of trolley moving together backwards
$v=0.2m{{s}^{-1}}$
For every 1 sec when the man moves ahead on the trolley, the trolley moves back by $0.2m$.
Hence in four seconds the man will move $4$ m but since the trolley moves back by $4\times 0.2=0.8m$
The displacement of man with respect to ground will be $4-0.8=3.2m$
Hence, the correct answer to the above question is option c.
Note:
The relative displacement with respect to ground is considered by considering the velocity of the other objects moving relative to you as zero. This condition is only possible in an inertial frame. Inertial frame is a non accelerating frame where no object is under acceleration.
Complete solution:
In the above case the man moves with some velocity and hence has some momentum. This momentum gets transferred to the trolley due the normal produced by the trolley due to a backward force by the foot.
Using law of conservation of momentum,
The forward momentum of the man = backward motion of the man and the trolley moving together.
Since momentum of an object is given by the product of mass times the velocity, i.e. mathematically given by p= mv $kgm{{s}^{-1}}$.
Mathematically we can represent the above condition as,
${{P}_{FORWARD}}={{P}_{BACKWARD}}$
Mass of the man is $80kg$ and moves with velocity of $1m{{s}^{-1}}$
Mass of man + Mass of trolley=$320+80=400kg$
Substituting in the above equation conservation of momentum,
${{P}_{FORWARD}}={{P}_{BACKWARD}}$
$80\times 1=400\times v$ where v is the velocity of trolley moving together backwards
$v=0.2m{{s}^{-1}}$
For every 1 sec when the man moves ahead on the trolley, the trolley moves back by $0.2m$.
Hence in four seconds the man will move $4$ m but since the trolley moves back by $4\times 0.2=0.8m$
The displacement of man with respect to ground will be $4-0.8=3.2m$
Hence, the correct answer to the above question is option c.
Note:
The relative displacement with respect to ground is considered by considering the velocity of the other objects moving relative to you as zero. This condition is only possible in an inertial frame. Inertial frame is a non accelerating frame where no object is under acceleration.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE