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If a body losses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest ? [AIEEE 2002]
- a)1 cm
- b)2cm
- c)3cm
- d)4cm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If a body losses half of its velocity on penetrating 3 cm in a wooden ...
Let the initial velocity of the body be u. Its velocity becomes u/2 after penetrating 3 cm in the block. We can calculate the deceleration of the body using these.
v2= u2 +2as
u2/4 = u2 + 2ax3
-3u2/4 = 6a
a = -u2/8
Now, we can calculate the distance the body travels till it comes to rest.
v2 = u2 + 2as
0 = u2 +2x(-u2/8)xs
u2 = u2s/4
s = 4 cm
Therefore, the body penetrates 1 cm (4-3=1cm) more before coming to rest.
I hope you understand the concept.
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If a body losses half of its velocity on penetrating 3 cm in a wooden ...
Given, the body loses half of its velocity on penetrating 3 cm in a wooden block. Let the initial velocity of the body be v and the distance it penetrates before coming to rest be x.
Using the formula for distance penetrated by a body in a medium, we have:
d = (1/2)mv^2/(Ffriction)
where d is the distance penetrated, m is the mass of the body, Ffriction is the frictional force acting on the body, and v is the initial velocity.
Since the body loses half of its velocity on penetrating 3 cm in a wooden block, we can write:
v/2 = (1/2)v - (Ffriction/m)(3 cm)
Simplifying, we get:
(Ffriction/m)x = (1/2)v
x = (m/2Ffriction)v
Now, we need to find the value of x. To do so, we need to know the value of the frictional force acting on the body.
Assuming that the frictional force is proportional to the velocity of the body, we can write:
Ffriction = kv
where k is a constant of proportionality.
Substituting this value of Ffriction in the equation for x, we get:
x = (m/2kv)v
x = (1/2k)m(v^2)
Since the distance penetrated is directly proportional to the square of the initial velocity, if the body loses half of its velocity, it will penetrate one-fourth of the distance it originally penetrated before coming to rest.
Hence, the body will penetrate 1 cm more before coming to rest. Therefore, option A is the correct answer.
Using the formula for distance penetrated by a body in a medium, we have:
d = (1/2)mv^2/(Ffriction)
where d is the distance penetrated, m is the mass of the body, Ffriction is the frictional force acting on the body, and v is the initial velocity.
Since the body loses half of its velocity on penetrating 3 cm in a wooden block, we can write:
v/2 = (1/2)v - (Ffriction/m)(3 cm)
Simplifying, we get:
(Ffriction/m)x = (1/2)v
x = (m/2Ffriction)v
Now, we need to find the value of x. To do so, we need to know the value of the frictional force acting on the body.
Assuming that the frictional force is proportional to the velocity of the body, we can write:
Ffriction = kv
where k is a constant of proportionality.
Substituting this value of Ffriction in the equation for x, we get:
x = (m/2kv)v
x = (1/2k)m(v^2)
Since the distance penetrated is directly proportional to the square of the initial velocity, if the body loses half of its velocity, it will penetrate one-fourth of the distance it originally penetrated before coming to rest.
Hence, the body will penetrate 1 cm more before coming to rest. Therefore, option A is the correct answer.
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