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A straight rod of length L has one of its end at the origin and the other at \({X}={L}\). If the mass per unit length of the rod is given by \({A}{x}\) where A is constant, where is its centre of mass?

Answer: B、C

\({x}_{{{C}{M}}}=\frac{{{\int_{{0}}^{{L}}}{x}{d}{m}}}{{{\int_{{0}}^{{L}}}{d}{m}}}=\frac{{{\int_{{0}}^{{L}}}{\left({X}\right)}{\left({A}{x}{\left.{d}{x}\right.}\right)}}}{{{\int_{{0}}^{{L}}}{\left({A}{x}{\left.{d}{x}\right.}\right)}}}=\frac{{2}}{{3}}{L}\)

\({x}_{{{C}{M}}}=\frac{{{\int_{{0}}^{{L}}}{x}{d}{m}}}{{{\int_{{0}}^{{L}}}{d}{m}}}=\frac{{{\int_{{0}}^{{L}}}{\left({X}\right)}{\left({A}{x}{\left.{d}{x}\right.}\right)}}}{{{\int_{{0}}^{{L}}}{\left({A}{x}{\left.{d}{x}\right.}\right)}}}=\frac{{2}}{{3}}{L}\)

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Calculate the energy released when 1000 small water drops each of same radius \({10}^{{-{7}}}{m}\) coalesce to form one large drop. The surface tension of water is \({7.0}\times{10}^{{-{2}}}{N}/{m}\).

A non-relativistic proton beam passes without deviation through a region of space where there are uniform transverse mutually perpendicular electric and magnetic fields with \({E}={120}{k}{V}{m}^{{-{{1}}}}{\quad\text{and}\quad}{B}={50}{m}{T}.\) Then the beam strikes a grounded target. Find the force which the beam acts on the target if the beam current is equal to \({i}={0.8}{m}{A}\).

Mass of protons \(={1.67}\times{10}^{{-{27}}}{k}{g}\).

Mass of protons \(={1.67}\times{10}^{{-{27}}}{k}{g}\).

Is it necessary for a transmitting antenna to be at the same height asthat of the receiving antanna for line of sight communication? A TV transmitting antenna is 81 m tall. How much service area can it cover, if the receiving antena is at the ground level?

The intensity of light pulse travelling in an optical fiber decreases according to the relation \({I}={I}_{{{0}}}{e}^{{-\alpha{x}}}\) . The intensity of light is reduced to \({20}\%\) of its initial value after a distance x equal to

(A) In\({\left(\frac{{{1}}}{{\alpha}}\right)}\)

(B) In\({\left(\alpha\right)}\)

(C) \(\frac{{{\left(\text{In}{5}\right)}}}{{\alpha}}\)

(D) In \({\left(\frac{{{5}}}{{\alpha}}\right)}\)

(A) In\({\left(\frac{{{1}}}{{\alpha}}\right)}\)

(B) In\({\left(\alpha\right)}\)

(C) \(\frac{{{\left(\text{In}{5}\right)}}}{{\alpha}}\)

(D) In \({\left(\frac{{{5}}}{{\alpha}}\right)}\)

Consider the following four statements (a-d) and select the options which includes all the correct ones only :-

(a) Transforming principle explained by Griffith was later identified as \(DNA\)

(b) Histones are rich in acidic amino acids lysines and arginines.

(c) In \(RNA\), every nucleotide has \(-OH\) group present at 2-position of ribose.

(d) In a \(ds DNA\) the two chains have antiparallel polarity. （ ）

(a) Transforming principle explained by Griffith was later identified as \(DNA\)

(b) Histones are rich in acidic amino acids lysines and arginines.

(c) In \(RNA\), every nucleotide has \(-OH\) group present at 2-position of ribose.

(d) In a \(ds DNA\) the two chains have antiparallel polarity. （ ）

A. Statements (b), (c) and (d)

B. Statements (a), (b)

C. Statements (b), (d)

D. Statements (a), (c) and (d)

The

sum of first 9 terms of the series \(\frac{{{1}^{{3}}}}{{1}}+\frac{{{1}^{{3}}+{2}^{{3}}}}{{{1}+{3}}}+\frac{{{1}^{{3}}+{2}^{{3}}+{3}^{{3}}}}{{{1}+{2}+{3}}}+.....\)

is

(1)

71 (2) 96 (3) 142 (4) 192

sum of first 9 terms of the series \(\frac{{{1}^{{3}}}}{{1}}+\frac{{{1}^{{3}}+{2}^{{3}}}}{{{1}+{3}}}+\frac{{{1}^{{3}}+{2}^{{3}}+{3}^{{3}}}}{{{1}+{2}+{3}}}+.....\)

is

(1)

71 (2) 96 (3) 142 (4) 192

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A heavy box of mass 20 kg is placed on a horizontal surface . If coefficient of kinetic friction between the box and the horizontal surface . Is 0.25 calculate the force of kinetic friction Also calculate acceleration produced under a force of 98 N applied horizontally ?

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