Variation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #11

The period of oscillation of a simple pendulum varies directly with the square root of the length. If the oscillation period of length `l` is `T`, then the oscillation period of length `4l` will be -
(a) `T`, (b) `2T`, (c) `T/2`, (d) `4T`
Ans: (b) `2T`
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Question No: #12

Fill in the blanks.:-
(i) If `y \propto \sqrt{x}`, then `x^3 \propto` ___.
(ii) If $ x \propto \sqrt[3]{y^2} $, then `y \propto` ___ .
(iii) If the radius and volume of a sphere is `r` and `V`, then, `V \propto` _______ .
(iv) If `x \propto y` and `x \propto z`, then `y+z \propto`_______ .
(v) If `A/B =` constant, then `A` varies ___ to `B`.
(vi) If `x \propto 1/y` and `y \propto 1/z`, then `x \propto` ___.
(vii) If `x \propto yz`, then `x` varies _______ as `y` and `z`.
Ans: (i) `y^6`, (ii) `x^\frac{3}{2}`, (iii) `r^3`, (iv) `x`, (v) Directly (সরল), (vi) `z`, (vii) Directly (সরল)
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Question No: #13

The statement is true or false:
(i) If `x` varies directly to `y`, then `xy =` constant.
(ii) If `A` varies inversely with `B`, then `A` varies directly with `1/B`.
(iii) If `A \propto C` when `B=` constant and `A \propto 1/B` when `C=` constant, then, `A \propto C/B` when `B` and `C` both vary.
(iv) If `x \propto 1/y`, then `(xy)^n =` constant.
(v) If `y \propto 1/x`, then, `y/x=` non-zero constant.
(vi) If `a \propto b, b \propto 1/c, c \propto d`, then `a` is inversely proportional to `d`.
(vii) If `x^2 \propto y`, then `y^2 \propto x`.
(viii) If `x \propto y^{3/2}`, then `y \propto x^{2/3}`.
(ix) If `x \propto z` and `y \propto z`, then `xy \propto z`.
(x) If `a \propto b` and `b \propto c`, then `(a+b) \propto c`.
Ans: (i) False, (ii) True, (iii) True, (iv) True, (v) False, (vi) True, (vii) False, (viii) True, (ix) True, (x) True
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Question No: #14

If `a \propto b^3` and $ b \propto \sqrt[3]{c} $, find the relation of variation between `a` and `c`.

Question No: #15

If `a \propto b` and `a \propto c`, then show that, `a \propto \sqrt{bc}`

Question No: #16

If `x \propto y` and `x \propto z` then show that, `x \propto (y-z)`

Question No: #17

If `x^2 \propto yz`, `y^2 \propto zx` and `z^2 \propto xy`, then find the relation among these variation constants.
Ans: Relation - product of three variation constants is 1
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Question No: #18

If `x \propto y`, `y \propto z` and `z \propto x`, then find the relation among these non-zero variation constants.

Question No: #19

If `y-z \propto 1/x`, `z-x \propto 1/y` and `x-y \propto 1/z`, then find the relation among these non-zero variation constants.
Ans: Sum of these constants is zero
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Question No: #20

If `(b-c) \propto bc, (c-a) \propto ca, (a-b) \propto ab`, then find the relation between the three variation constants.
Ans: Sum of these constants is zero
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