mcq
Abody is dropped from the top of a tower and falls free, then which of the following is/are correct
(A) The distance covered by it after n seconds is directly proportional to na
(B) The distance covered in the nth second is proportional to 2n - 1
(C) The velocity of the body after n seconds is proportional to n
(D) The distance covered in the nth second is proportional to n
Answers
Given : A body is dropped from the top of a tower and falls free,
To Find : which of the following is/are correct
(A)The distance covered by it after n seconds is directly proportional to n²
(B)The distance covered in the nth second is proportional to 2n−1
(C)The velocity of the body after n seconds is proportional to n
(D)The distance covered in the nth second is proportional to n
Solution:
u = 0
V = u + at
Velocity after n secs
V = 0 + an
=> V = an
=> V ∝ n
Hence velocity of the body after n seconds is proportional to n
Distance covered in nth Second
= Sₙ - Sₙ₋₁
S = ut + (1/2)at²
= un + (1/2)a(n)² - u(n-1) + (1/2)a(n-1)²
u = 0
= (1/2)a ( n² - (n - 1)²)
= (1/2)a (2n - 1)(1)
= (a/2)(2n - 1)
S ∝ (2n - 1)
The distance covered in the nth second is proportional to 2n−1
Distance covered in n seconds
S = (1/2)an² as u = 0
=> S ∝ n²
Hence The distance covered by it after n seconds is directly proportional to n²
3 options are correct
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