Question

An object weighing 10 N is dropped from a height of 4 meters above the ground.When it has fallen freely through a distance of 1 meter, its total mechanical energywith respect to the ground is *



a)2.5 J

b)10 J

c)30 J

d)40 J

​

Answer 1

Answer:

2.5 J IS CORRECT ANSWER

Answer 2

the correct option is d) 40 J

given

W = 10N

H=4m (height from which the object is thrown)

h=1m ( distance travelled by an object after dropping)

to find

total mechanical energy w.r.t   the ground

solution

• potential energy is given by:

V = mgh

where V = potential energy of the object

m is the mass of the object

h is the height of the object from the ground = 3 m

V=10 X 3

V=30J

• the kinetic energy of the body at this point is:

K = $1/2mv^{2}$

where K is kinetic energy

m is the mass of the body

v = velocity of the body at that point

now W = 10N

W = mg = 10N

m  X 10 = 10N ( because g=10m/s^2)

m=1kg -------(i)

• applying newton's third equation of motion

$v^{2} -u^{2} =2aS$

where,

v is the final velocity of the object i.e the velocity attained by the object after falling through a distance of 1 m

u = initial velocity which is zero

a is the acceleration due to gravity =10m/s^2

S is the distance traveled = 1m

$v^{2}$ = 2 X 10 X 1

$v^{2}$=20m/s---------(ii)

• now applying (i) and (ii) in the kinetic energy formula, we get:

K = 1/2 X 1 X 20

K = 10J

• total mechanical energy with respect to ground is given by adding the object's potential energy and kinetic energy at that point.

• so E = V + K

E = 30 + 10

E = 40J

the correct option is d) 40 J

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