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If in a hypothetical system if the angular momentum and mass a

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If in a hypothetical system if the angular momentum and mass are dimensionless. Then which of the following is true.

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Practice questions from similar books

Question 1

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I,

x^{2} + y^{2} = a

, (i),

m y = m^{2} x + a

, (P),

(\frac{a}{m ^{2}}, \frac{2 a}{m})

II,

x^{2} + a^{2} y^{2} = a

, (ii),

y = m x + a m^{2} + 1

, (Q),

(\frac{- m a}{m ^{2} + 1}, \frac{a}{m ^{2} + 1})

III,

y^{2} = 4 a x

, (iii),

y = m x + a^{2} m^{2} - 1

, (R),

(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{1}{a ^{2} m ^{2} + 1})

IV,

x^{2} - a^{2} y^{2} = a^{2}

, (iv),

y = m x + a^{2} m^{2} + 1

, (S),

(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{- 1}{a ^{2} m ^{2} + 1})

The tangent to a suitable conic (Column 1) at

(3, \frac{1}{2})

is found to be

3 x + 2 y = 4,

then which of the following options is the only CORRECT combination?(IV) (iii) (S) (b) (II) (iii) (R)(II) (iv) (R) (d) (IV) (iv) (S)

View solution

Question 2

Let

g : R \to R

be a differentiable function with

g (0) = 0, g^{'} (1) = 0, g^{'} (1) \neq = 0

.Let

f (x) = {\frac{x}{∣ x ∣} g (x), 0 \neq = 0 and 0, x = 0

and

h (x) = e^{∣ x ∣}

for all

x \in R

. Let

(f o h) (x)

denote

f (h (x)) and (h o f) (x)

denote

h (f (x))

. Then which of thx!=0 and e following is (are) true?

View solution

Question 3

From a point

P (λ, λ, λ)

, perpendicular PQ and PR are drawn respectively on the lines

y = x, z = 1

and

y = - x, z = - 1

.If P is such that

∠ Q P R

is a right angle, then the possible value(s) of

λ

is/(are)

View solution

Question 4

Consider the family of all circles whose centers lie on the straight line `y=x`. If this family of circles is represented by the differential equation `P y^(primeprime)+Q y^(prime)+1=0,`where `P ,Q`are functions of `x , y`and `y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)),`then which of the following statements is (are) true?(a)`P=y+x`(b)`P=y-x`(c)`P+Q=1-x+y+y^(prime)+(y^(prime))^2`(d)`P-Q=x+y-y^(prime)-(y^(prime))^2`

View solution

Question Text

If in a hypothetical system if the angular momentum and mass are dimensionless. Then which of the following is true.

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