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51.

When a disc is rotating with angular velocity `omega` , a particle situated at a distance of 4 cm just begins to slip . If the angular velocity is doubled , at what distance will the particle start to slip ?A. 1 cmB. 2 cmC. 3 cmD. 4 cm

Answer» Correct Answer - A
Angular velocity = `omega`
Centripetal force F = `mr omega^(2)`
or `r prop (1)/(omega^(2))`
`therefore (r_(1))/(r_(2)) = (omega_(2)^(2))/(omega_(1)^(2))`
or `(4)/(r_(2)) = (4omega^(2))/(omega^(2))`
or `r_(2) = 1` cm
Discussion
52.

Moment of inertia of a uniform circular disc about a diameter is `I`. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be.A. `6 I`B. 4 IC. 2 ID. 8 I

Answer» Correct Answer - A
Moment of inertia of a disc about a diameter is `(1)/(4) MR^(2) = I " " `(given)
`therefore MR^(2) = 4I`
Now , required moment of inertia = `(3)/(2) MR^(2)`
`= (3)/(2) (4I) = 6 I`
Discussion
53.

The isotope that causes skin disease isA. `I^(131)`B. `S^(35)`C. `p^(31)`D. None of these

Answer» Correct Answer - B
`S^(35)` , an stable isotope of sulphur , when present outside the body , causes skin infection .
Discussion
54.

The first order integrated rate equation isA. `k = (x)/(t)`B. `k = - ""(2.303)/(t) "log" (a)/(a-x)`C. `k = (1)/(t) "ln" (a)/(a-x)`D. `k =(1)/(t) (x)/(a(a-x))`

Answer» Correct Answer - C
For first order ,
rate = `(d[R])/(dt) = k[R]`
or `(d[R])/([R]) = kdt " " … (i)`
On integration Eq. (i)
`int (d[R])/([R]) = k int dt`
In [R] = `-kt + C " " … (ii)`
At t = 0 , [R] = `[R_(0)]`
[where , R = final concentration , ie , a - x and `R_(0)` is the initial concentration ie,a ]
In `[R_(0)] = C`
On putting the value of C in Eq. (ii) we get
ln[R] = -kt + ln `[R_(0)]`
`-kt ` = ln [R] - ln `[R_(0)]`
kt = ln `[R_(0)] - `ln [R]
or `k = (1)/(t)` ln `([R_(0)])/([R])`
or `k = (1)/(t) "ln" (a)/(a-x)`
Discussion
55.

For the formation of terylene the number of moles of ehtylene glycol required per mole of terephthalic acid isA. 1B. 2C. 3D. 4

Answer» Correct Answer - A
For the preparation of terylene , n moles of glycol are required for n moles of terephthalic acid .
`therefore` Per mole of terephthalic acid , moles of ethylene glycol required is = 1
Discussion
56.

For a thermocouple , the inversion temperature is `600^(@)C`and the neutral temperature is `320^(@)C` . Find the temperature of the cold junction ?A. `40^(@)C`B. `20^(@)C`C. `80^(@)C`D. `60^(@)C`

Answer» Correct Answer - A
Neutral temperature `T_(n) = (T_(c) + T_(i))/(2)`
`320^(@) = (T_(c) + 600^(@))/(2)`
`640^(@) = T_(c) + 600^(@)`
`T_(c) = 40^(@)C`
Discussion
57.

the equations of the tangents to `9x^2+16y^2=144 ,` which make equal intercepts on the coordinate axes.A. x + y = 5B. x + y = 16C. x + y = 15D. None of these

Answer» Correct Answer - A
Given curve is `9x^(2) + 16y^(2) = 144`
`implies (x^(2))/(16) + (y^(2))/(9) = 1 `
Let the equation of tangent is x + y = k
`implies y = -x + k`
It is a tangent to the given curve if
`c^(2) = a^(2) m^(2) + b^(2)`
`implies k^(2) = 16(-1)^(2) + 9`
`implies k^(2) = 25`
`implies k = pm 5`
`therefore` Required equation of tangent are
`x + y = pm5`
Discussion
58.

Find the point where the line `(x-1)/2=(y-2)/-3=(z+3)/4` meets the plane `2x+4y-z=1`.A. (3,-1,1)B. (3,1,1)C. (1,1,3)D. (1,3,1)

Answer» Correct Answer - A
Let point be (a , b , c) then
2a + 4b - c = 1 `" " …. (i)`
and a = 2k + 1 , b = -3k + 2 and c = 4k - 3
(where k is constant )
On substituting these values in Eq. (i) , we get
2(2k + 1) + 4(-3 k + 2)- (4k - 3) = 1
`implies k = 1`
Hence , required point is (3 , -1 , 1) .
Discussion
59.

The pressure of a gas is 100 k Pa. if it is compressed from 1 `m^(3)` to `10 dm^(3)` , find the work done .A. `990 J`B. 9990 JC. 9900 JD. 99000 J

Answer» Correct Answer - D
Given ,
pressure , `p = 100 k Pa = 10^(5)` Pa
Initial volume , `V_(1) = 1m^(3)`
Final volume , `V_(2) = 10 xx 10^(-3) m^(3) = 10^(-2) m^(3)`
W = `p Delta V`
`=10^(5) (1 - 10^(-2)) = 99,000 J`
Discussion
60.

If the density of the earth is doubled keeping its radius constant then acceleration due to gravity will be `(g=9.8 m//s^(2))`A. `9.8 m//s^(2)`B. `19.6 m//s^(2)`C. `4.9 m//s^(2)`D. `39.2 m//s^(2)`

Answer» Correct Answer - B
Discussion
61.

The increase in pressure required to decrease the 200 L volume of a liquid by 0.008 % in kPa is (Bulk modulus of the liquid = 2100 M Pa is )A. 8.4B. 84C. 92.4D. 168

Answer» Correct Answer - B
Bulk modulus `K = (Deltap)/(DeltaV) * V`
`Deltap = (K Delta V)/(V)`
`Deltap = (2100 xx 10^(6) xx 0.008)/(200)`
= 84kpa
Discussion
62.

With an increase in temperature , surface tension of liquid (except molten copper and cadmium)A. increasesB. remain sameC. decreasesD. first decreases then increases

Answer» Correct Answer - C
The surface tension of liquid decreases with rise of temperature . The surface tension of liquid is zero at its boiling point and it vanishes at critical temperature . At critical temperature intermolecular forces for liquid and gases becomes equal and liquid can expand without any restriction . for small temperature differences , the variation in surface tension with temperature is linear and is given by relation
`T_(t) = T_(0) (1 - alpha t)`
where `T_(t) , T_(0)` are the surface tension at `t^(@)C` and `0^(@)C` respectively and `alpha` is the temperature coefficient of surface tension.
Discussion