wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The weight of a body of mass m decreases by 1% when it is raised to a height h above the earth's surface. If the body is taken to a depth h in a mine, the change in its weight is


A

0.5% decrease.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

2% decrease.

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

0.5% increase.

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

1% increase.

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

0.5% decrease.


Step 1: Given data

The weight of a body of mass m decreases by 1% when it is raised to a height h above the earth's surface

Step 2: To find

The change in weight if the body is taken to a depth h in a mine.

Step 3: Formula used

Acceleration due to gravity at a height h,

g'=g1-2hR

Acceleration due to gravity at a depth h,

g''=g1-hR

where R is radius of earth.

Step 4: Calculation

Acceleration due to gravity when the body is raised to a height h,

g'=g1-2hR

Given that the weight of the body decreases by 1% in this case.

Therefore, weight of the body at a height h,

w'=mg'w'=mg1-2hR

Original weight of the body,

w=mg

Since it is given that the weight decreases by 1%,

w'=99100×wmg1-2hR=99100×mg1-2hR=991002hR=1-991002hR=1100h=R200

When the body is taken to a depth h,

Acceleration due to gravity,

g''=g1-hR

weight in this case,

w''=mg''w''=mg1-hRw''=mg1-R200Rh=R200w''=mg1-1200w''=mg199200w''=199200ww''=99.5100w

Here the weight at depth h is 99.5% of the initial weight.

Therefore, the weight decreases by 0.5%.

Option A is correct.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Variation in g
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon