Question

1.The same horizontal force, of magnitude F, is applied to two different blocks, of mass m and 3m The blocks move on a frictionless surface and both blocks begin from rest. If each block moves the same distance as the force is applied, which one of the following sentences is true?

A)The lighter block acquires 9 times as much kinetic energy as the heavier block.

B)The two blocks acquire the same kinetic energy.

C)The heavier block acquires 3 times as much kinetic energy as the lighter block.

D)The lighter block acquires 3 times as much kinetic energy as the heavier block.

E)The heavier block acquires 9 times as much kinetic energy as the lighter block.

Note: I initially came up with C as my answer, but it is supposably wrong.

1.1 Two identical objects of the same mass, initially at rest, are accelerated through the same distance by different forces such that one object gains velocity twice that of the other object. One can conclude that the force on the faster object is _________

A)10 times that of the slower object

B)Half that of the slower object

C)16 times that of the slower object

D)Twice that of the slower object

E)Four times that of the slower object.   

F)Three times that of the slower object

Please help and explain as I want to understand the question and answer. Thank you.

Answer 1

1

According to Work energy theorum, the Work done on an object will be converted to Kinetic Energy. That is ;

Work Done,

In our case, the Force (F) and displacement (s) is same, so the kinetic energy acquired by both blocks will be equal.

Here, it does not depend on the mass of blocks

Option ( B )

1.1

From Newtons second law, Force is given by product of mass and acceleration.

From equations on motion,  

Since the body is initially at rest, u = 0

Rearranging : Acceleration :

Subtituting Eqn (2) on Eqn (1) :

Since mass ( m ) and distance ( s ) are same

  

That is a direct square relation between Force and velocity. That is if velocity twice that of the other object, the force will be   , That is 4 times

Option ( E )