Physics
General
Easy

Question

At what distance from the center of earth, the value of acceleration due to gravity g will be half that of the surfaces  (R=Radius of earth)

  1. 2R
  2. R
  3. 1.414R
  4. 0.414R

The correct answer is: 1.414R

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The length of the subtangent (if exists) at any point θ on the ellipse x squared over a squared minus y squared over b squared equals 1 is

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The radii of two planets are respectively R1 and R2 and their densities are respectively rho subscript 1 and rho subscript 2 the ratio of the accelerations due to gravity at their surface is……

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A body weight 500 N on the surface of the earth. How much would it weight half way below the surface of earth

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Following two isomers are

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It has chiral centre (*). It is-

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Let g be the acceleration due to gravity at earth's surface and k be the rotational K.E of earth suppose the earth's radius decreases by 2% keeping alt other quantities same then

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The sum of the subtangent and subnormal to the curve  at x equals c left square bracket 2 cos invisible function application theta minus log invisible function application left parenthesis cos invisible function application e c theta plus cot invisible function application theta right parenthesis right square bracket comma y equals c sin invisible function application 2 theta text  at  end text theta equals pi over 3 is

x = c[2cosθ - log(cosecθ + cotθ)
y = csin2θ
A tangent to the curve is given by the slope at the point. The slope is given by fraction numerator d y over denominator d x end fraction
let's differentiate x w.r.t θ.
x equals c left square bracket 2 cos theta minus log left parenthesis cos e c theta plus c o t theta right parenthesis
fraction numerator d x over denominator d theta end fraction space equals space c left square bracket 2 left parenthesis negative sin theta right parenthesis space minus space fraction numerator 1 over denominator cos e c theta space plus space c o t theta end fraction fraction numerator d over denominator d theta end fraction cos e c theta space plus c o t theta
space space space space space space space space equals c left square bracket negative 2 sin theta space minus space fraction numerator left parenthesis negative cos e c theta c o t theta space minus cos e c squared theta right parenthesis over denominator cos e c theta space plus space c o t theta end fraction
space space space space space space space equals c left square bracket negative 2 sin theta space minus left parenthesis negative cos e c theta right parenthesis fraction numerator c o t theta space plus space cos e c theta over denominator cos e c theta space plus space c o t theta end fraction right square bracket
space space space space space space equals c left square bracket negative 2 sin theta space plus space cos e c theta right square bracket

space space spaceWe will differentiate y w.r.t θ
y equals c sin 2 theta
fraction numerator d y over denominator d theta end fraction space equals space c cos 2 theta space fraction numerator d over denominator d theta end fraction 2 theta
space space space space space space space space equals 2 c cos 2 theta
Now, let us denote slope by mm space equals fraction numerator d y over denominator d x end fraction
space space space space space equals space fraction numerator d y over denominator d theta end fraction cross times fraction numerator d theta over denominator d x end fraction
space space space space space equals 2 c cos 2 theta space cross times space fraction numerator 1 over denominator c left square bracket negative 2 sin theta space plus space cos e c theta right square bracket end fraction
left parenthesis m right parenthesis subscript theta equals pi over 3 space end subscript equals 2 c cos left parenthesis fraction numerator 2 pi over denominator 3 end fraction right parenthesis space cross times space fraction numerator 1 over denominator c left square bracket negative 2 sin begin display style pi over 3 end style plus cos e c begin display style straight pi over 3 end style right square bracket end fraction
space space space space space space space space space space space space space space space equals fraction numerator 2 c left parenthesis negative begin display style 1 half end style right parenthesis over denominator c left parenthesis negative 2 cross times begin display style fraction numerator square root of 3 over denominator 2 end fraction end style plus begin display style fraction numerator 2 over denominator square root of 3 end fraction end style right parenthesis space space space space space space space space space end fraction space space space... left curly bracket cos fraction numerator 2 pi over denominator 3 end fraction equals cos left parenthesis pi minus straight pi over 3 right parenthesis equals negative 1 half right curly bracket
space space space space space space space space space space space space space space equals fraction numerator negative 1 over denominator negative square root of 3 plus begin display style fraction numerator 2 over denominator square root of 3 end fraction end style end fraction
space space space space space space space space space space equals space space minus fraction numerator square root of 3 over denominator negative 3 space plus space 2 end fraction
space space space space space space
space space space

space space space space space space
m = √3
y=(y)θ=π/3c sin fraction numerator 2 pi over denominator 3 end fraction
y subscript 1 equals c sin pi over 3 space space space... left curly bracket sin fraction numerator 2 pi over denominator 3 end fraction space equals sin left parenthesis pi minus pi over 3 right parenthesis space equals sin pi over 3 right curly bracket
space space space space equals c space cross times space fraction numerator square root of 3 over denominator 2 end fraction
space space space space equals fraction numerator square root of 3 over denominator 2 end fraction c
L e n g t h space o f space s u b n o r m a l equals open vertical bar y subscript 1 m close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open vertical bar fraction numerator square root of 3 over denominator 2 end fraction c space cross times space square root of 3 close vertical bar

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open vertical bar 3 over 2 c close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 over 2 c

space
L e n g t h space o f space s u b tan g e n t space equals open vertical bar y subscript 1 over m close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open vertical bar fraction numerator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style c over denominator square root of 3 end fraction close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half c
L e n g t h space o f space s u b tan g e n t space plus space l e n g t h space o f space s u b n o r m a l space equals fraction numerator 3 c over denominator 2 end fraction plus fraction numerator 1 c over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 4 c over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 cSo, the answer is 2c

The sum of the subtangent and subnormal to the curve  at x equals c left square bracket 2 cos invisible function application theta minus log invisible function application left parenthesis cos invisible function application e c theta plus cot invisible function application theta right parenthesis right square bracket comma y equals c sin invisible function application 2 theta text  at  end text theta equals pi over 3 is

Maths-General
x = c[2cosθ - log(cosecθ + cotθ)
y = csin2θ
A tangent to the curve is given by the slope at the point. The slope is given by fraction numerator d y over denominator d x end fraction
let's differentiate x w.r.t θ.
x equals c left square bracket 2 cos theta minus log left parenthesis cos e c theta plus c o t theta right parenthesis
fraction numerator d x over denominator d theta end fraction space equals space c left square bracket 2 left parenthesis negative sin theta right parenthesis space minus space fraction numerator 1 over denominator cos e c theta space plus space c o t theta end fraction fraction numerator d over denominator d theta end fraction cos e c theta space plus c o t theta
space space space space space space space space equals c left square bracket negative 2 sin theta space minus space fraction numerator left parenthesis negative cos e c theta c o t theta space minus cos e c squared theta right parenthesis over denominator cos e c theta space plus space c o t theta end fraction
space space space space space space space equals c left square bracket negative 2 sin theta space minus left parenthesis negative cos e c theta right parenthesis fraction numerator c o t theta space plus space cos e c theta over denominator cos e c theta space plus space c o t theta end fraction right square bracket
space space space space space space equals c left square bracket negative 2 sin theta space plus space cos e c theta right square bracket

space space spaceWe will differentiate y w.r.t θ
y equals c sin 2 theta
fraction numerator d y over denominator d theta end fraction space equals space c cos 2 theta space fraction numerator d over denominator d theta end fraction 2 theta
space space space space space space space space equals 2 c cos 2 theta
Now, let us denote slope by mm space equals fraction numerator d y over denominator d x end fraction
space space space space space equals space fraction numerator d y over denominator d theta end fraction cross times fraction numerator d theta over denominator d x end fraction
space space space space space equals 2 c cos 2 theta space cross times space fraction numerator 1 over denominator c left square bracket negative 2 sin theta space plus space cos e c theta right square bracket end fraction
left parenthesis m right parenthesis subscript theta equals pi over 3 space end subscript equals 2 c cos left parenthesis fraction numerator 2 pi over denominator 3 end fraction right parenthesis space cross times space fraction numerator 1 over denominator c left square bracket negative 2 sin begin display style pi over 3 end style plus cos e c begin display style straight pi over 3 end style right square bracket end fraction
space space space space space space space space space space space space space space space equals fraction numerator 2 c left parenthesis negative begin display style 1 half end style right parenthesis over denominator c left parenthesis negative 2 cross times begin display style fraction numerator square root of 3 over denominator 2 end fraction end style plus begin display style fraction numerator 2 over denominator square root of 3 end fraction end style right parenthesis space space space space space space space space space end fraction space space space... left curly bracket cos fraction numerator 2 pi over denominator 3 end fraction equals cos left parenthesis pi minus straight pi over 3 right parenthesis equals negative 1 half right curly bracket
space space space space space space space space space space space space space space equals fraction numerator negative 1 over denominator negative square root of 3 plus begin display style fraction numerator 2 over denominator square root of 3 end fraction end style end fraction
space space space space space space space space space space equals space space minus fraction numerator square root of 3 over denominator negative 3 space plus space 2 end fraction
space space space space space space
space space space

space space space space space space
m = √3
y=(y)θ=π/3c sin fraction numerator 2 pi over denominator 3 end fraction
y subscript 1 equals c sin pi over 3 space space space... left curly bracket sin fraction numerator 2 pi over denominator 3 end fraction space equals sin left parenthesis pi minus pi over 3 right parenthesis space equals sin pi over 3 right curly bracket
space space space space equals c space cross times space fraction numerator square root of 3 over denominator 2 end fraction
space space space space equals fraction numerator square root of 3 over denominator 2 end fraction c
L e n g t h space o f space s u b n o r m a l equals open vertical bar y subscript 1 m close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open vertical bar fraction numerator square root of 3 over denominator 2 end fraction c space cross times space square root of 3 close vertical bar

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open vertical bar 3 over 2 c close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 over 2 c

space
L e n g t h space o f space s u b tan g e n t space equals open vertical bar y subscript 1 over m close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open vertical bar fraction numerator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style c over denominator square root of 3 end fraction close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half c
L e n g t h space o f space s u b tan g e n t space plus space l e n g t h space o f space s u b n o r m a l space equals fraction numerator 3 c over denominator 2 end fraction plus fraction numerator 1 c over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 4 c over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 cSo, the answer is 2c
parallel
General
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Which is a pair of geometrical isomers ?

Which is a pair of geometrical isomers ?

chemistry-General
General
chemistry-

are-

are-

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Assuming earth to be a sphere of a uniform density, what is value of gravitational acceleration. in mine 100 km below the earth surface .... ms-2

Assuming earth to be a sphere of a uniform density, what is value of gravitational acceleration. in mine 100 km below the earth surface .... ms-2

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