Question

Two blocks of ice, one four times as heavy as the other, are at rest on a frozen lake. A person pushes each block the same distance d. Ignore friction and assume that an equal force F is exerted on each block.
Now assume that both blocks have thesame speed after being pushed with the same force F. What can be said about the distances the two blocks arepushed?

A. The heavyblock must be pushed 16 times farther than the lightblock.
B. The heavyblock must be pushed 4 times farther than the lightblock.
C. The heavyblock must be pushed 2 times farther than the lightblock.
D. The heavytblock must be pushed the same distance as the lightblock.
E. The heavyblock must be pushed half as far as the light block.

Answer 1

Answer:b

Explanation:

Given

mass of heavy object is 4m

mass of lighter object is m

A person pushes each block  with same force F

According to Work Energy theorem Change in kinetic energy of object is equal to Work done by all the object

As launching velocity is same for both the object so heavier mass must possess greater kinetic energy . For same force heavier mass must be pushed 4 times farther than the light block .

$\Delta (K.E.)_H=\frac{1}{2}(4m)v^2$

$\Delta (K.E.)_L=\frac{1}{2}(m)v^2$

$\Delta K.E.=F\times d$

So the correct option is b