Conversion of Units

Q. Sixty-four drops are joined together to form a bigger drop. If each small drop has a capacitance $C$, a potential$V$, and a charge $q$, then the capacitance of the bigger drop will be

1. $64c$
2. $4c$
3. $c$
4. $16c$

Q. Find the centre of mass of a uniform:
(a) Half-disc
(b) Quarter-disc

Q. The potential energy of interaction between the semicircular ring of mass $M$ and radius $R$, and the particle of mass$M$ placed at the centre of curvature of the semicircular arc is

1. $-\frac{G{M}^2}{R}$
   
2. $-\frac{2G{M}^2}{R}$
3. $-\frac{G{M}^2}{\pi R}$
4. none of these

Q.

A neutron star has a density equal to that of the nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass is 4.0 $\times {10}^{30}$ kg (twice the mass of the sun).

Q. A ring of mass $M$ and radius $R$ lies in $x-y$ plane with its centre at origin as shown. The mass distribution of ring is nonuniform such that at any point 𝑃 on the ring, the mass per unit length is given by $\lambda ={\lambda }_0{\cos }^2\theta$ where ${\lambda }_0$ is a positive constant). Then the moment of inertia of the ring about $z$-axis is:

1. $\frac{1}{2}\frac{M}{{\lambda }_0}R$
2. $M{R}^2$
3. $\frac{1}{2}M{R}^2$
4. $\frac{1}{\pi }\frac{M}{{\lambda }_0}R$

Q. The density of a material in $SI$ units is $128kg{m}^{-3}$. In certain units in which the unit of length is $25cm$ and the unit of mass is $50g$, the numerical value of density of the material is

1. $410$
2. $16$
3. $40$
4. $640$

Q. Find the area of a square whose side is
(a) 15 cm
(b) 55 cm

Q. A tank can hold $50$ litres of water.At present, it is only $30\%$ full.How many litres of water shall I put in to the tank so that it becomes $50\%$ full?

Q. What is the energy of state in a triply ionised berrylium $\left(B{e}^{+++}\right)$ whose radius is equal to that of ground state of hydrogen?

1. 54.4 eV
2. 27.2 eV
3. 13.6 eV
4. 40.8 eV

Q. How many students have their height less than 140 cm ?

1. $31$
2. $33$
3. $32$
4. $34$

Q. The dimension of $\frac{1}{2}{\epsilon }_0{E}^2$, where ${\epsilon }_0$ is permittivity of free space and $E$ is electric field, is

1. $M{L}^2{T}^{-2}$
2. $M{L}^2{T}^{-1}$
3. $ML{T}^{-1}$
4. $M{L}^{-1}{T}^{-2}$

Q.

How to convert the

N m² Kg^-2 is equals to cm³ S^-2 g-1

Is there any table to convert these kinds of things in easy manner

Plz tell me

Q. A traffic survey conducted on Wednesday in the month of February from 7:00 to 1:00 pm indicates that 1250 vehicles passed through the certain location of roadway. The expansion factor for conducted survey is 10. The daily expansion factor for wednesday is 7.3 and monthly expansion factor for february is 1.2. The annual average daily traffic would be__

1. 15640

Q. A total of 4900 joules was expended in lifting a 50 kg mass, then the mass was raised to a height of :

1. 98m
2. 960m
3. 245m
4. 10m

Q. If $200MeV$ energy is released in the fission of a single $U^{235}$ nucleus, the number of fissions require per second to produce a $1$ kilowatt power shall be $(Given1eV=1.6\times {10}^{-19}J)$

1. $3.125\times {10}^{14}$
2. $3.125\times {10}^{13}$
3. $3.125\times {10}^{15}$
4. $3.125\times {10}^{16}$

Q. A nucleus splits into two nuclear parts which have their velocity ratio equal to $2:1$. What will be the ratio of their nuclear radius

1. $3^{1/2}:1$
2. $2^{1/3}:1$
3. ${1:2}^{1/3}$
4. ${1:3}^{1/2}$

Q. A boat having a length of 3 metre and breadth 2 metre is floating on a lake. The boat sinks by one cm when a man gets on it. The mass of the man is:

1. 60 kg
2. 62 kg
3. 72 kg
4. 128 kg

Q. Speed of flow of water in a river is $3m/s$. Speed of man in water is $5m/s$. If the man want to cross the river in shortest time, then he has to head

1. Normal to bank of river
2. ${37}^{\circ }$ to the bank of river
3. ${53}^{\circ }$ to the bank of the river
4. along the bank of the river

Q. From four corners of a rectangular iron sheet of $24$ cm $\times 30$ cm, four squares of side $6$ cm are cut. The remaining portion of the sheet is formed into an open box. The internal volume (in cm${}^3$) of the box is

1. $4300$
2. $2590$
3. $2542$
4. $1296$

Q. A wheel completes $3500$ revolutions to cover $22km$ distance. The diameter of the wheel is

1. $1m$
2. $1.5m$
3. $2m$
4. $0.5m$

Q. Measure the hair of other members of your family.

Q. The mass defect in a particular nuclear reaction is $0.3grams$. The amount of energy liberated in kilowatt hour is: (Velocity of light = $3\times {10}^{8}m/s$)

1. $1.5\times {10}^6$
2. $3\times {10}^6$
3. $7.5\times {10}^6$
4. $2.5\times {10}^6$

Q. Two girls weigh 30 Kg and 29 Kg respectively. what is their total weight?

Q. A boat can go $65km$ upstream in $5$ hours and $69km$ downstream in $3$ hours. Find the speed of stream.

1. $13km/hr.$
2. $6km/hr.$
3. $7km/hr.$
4. $5km/hr.$

Q. What is $52$ inches in meters ?

Q. Bullets are fired in an field in 360°with a speed U.Find the maximum area by the bullets

Q. Convert the following quantity as indicated:
$0.2cm=............mm$

Q. The activity of a sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in one hour. The activity after $3$ hours more will be

1. $\frac{A_0}{3\sqrt{3}}$
2. $\frac{A_0}{9}$
3. $\frac{A_0}{9\sqrt{3}}$
4. $\frac{A_0}{27}$