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1.	A liquid drop having surface energy E is spread into 512 droplets of same size. The final surface energy of the droplets isA. 2 EB. 4EC. 8ED. 12 E
Answer» Correct Answer - C `(E_(2))/(E(1))=n^(1//3)` `(E_(2))/(E_(1))=512^(1//3)` `E_(2)=8E`

2.	Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1:3. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched isA. `3:1`B. `9:1`C. `27:1`D. `81:1`
Answer» Correct Answer - D `L_(1)=L_(2),y_(1)=y_(2),f_(1)=f_(2),(d_(1))/(d_(2))=(1)/(2),(u_(1))/(u_(2))=?` `(u_(1))/(u_(2))=(1)/(2)("stress")/(y)=(F^(2))/(d_(1)^(4))xx(d_(2)^(4))/(F_(1)^(2))=((d_(2))/(d_(1)))=(81)/(1)`

3.	If the end correction of an open pipe is 0.8 cm, then the inner radius of that pipe will beA. `(1)/(3)cm`B. `(2)/(3)cm,`C. `(3)/(2)cm`D. 0.2cm
Answer» Correct Answer - B r=0.6d 8.0=0.6d `d=(8)/(6)=(4)/(3)` `r=(d)/(2)=(4)/(2xx3)=(2)/(3)cm`

4.	When open pipe is closed from one end, then third overtone of closed pipe is higher in frequency by 150 Hz than second overtone of open pipe. The fundamental frequency of open end pipe will beA. 75 HzB. 150 HzC. 225 HzD. 300 Hz
Answer» Correct Answer - D `n_(3)-n_(2)=150` `7n_(c)-3n_(0)=150` `7n_(c)-3xxn_(0)=150` `7n_(c)-6n_(c)=150` `n_(c)=150` But, `n_(0)=2n_(c)` `:.n_(0)=2xx150=300Hz.`

5.	A black rectangular surface of area A emits energy E per second at `27^circC`. If length and breadth are reduced to one third of initial value and temperature is raised to `327^circC`, then energy emitted per second becomesA. `(4E)/(9)`B. `(7E)/(9)`C. `(10E)/(9)`D. `(16E)/(9)`
Answer» Correct Answer - D `T_(1)=27+273=300K,L_(2)=(1)/(3)L_(1)` `T_(2)=273+32=600K` `(E_(2))/(E_(1))=(A_(2))/(A_(1))((T_(2))/(T_(1)))^(4)` `=(L_(2)b_(2))/(L_(1)b_(1))xx((600)/(300))^(4)` `=(1)/(3)xx(1)/(3)=16` `E_(2)=(16)/(9)E_(1)`.

6.	Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure isA. `[(1)/(3)]^(rd)` kinetic energy per unit volume of a gasB. `[(2)/(3)]^(rd)` kinetic energy per unit volume of a gasC. `[(3)/(4)]^(th)` kinetic energy per unit volume of a gasD. `(3)/(2)xx` kinetic energy per unit volume of a gas
Answer» Correct Answer - B `P=(1)/(3)pC^(2)=(1)/(3)(M)/(V)C^(2)=(2)/(3)xx((1)/(2)MC^(2))/(V)` `=((2)/(3))^(rd)` kinetic energy per unit volume.

7.	In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point isA. 5B. 2C. `0.5`D. `0.2`
Answer» Correct Answer - D `(KE_(H))/(KE_(L))=((1)/(2)mv_(H)^(1))/((1)/(2)mv_(L)^(2))=(rg)/(5rg)=0.2`

8.	Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:A. `-(4Gm)/(r)`B. `-(8Gm)/(r)`C. `-(16Gm)/(r)`D. `-(32Gm)/(r)`
Answer» Correct Answer - C `(M)/(m)=((x)/(2-x))^(2)` `9=((x)/(r-x))^(2)` `3=(x)/(r-x)` `3r-3x=x` `3r=4x` `x=(3)/(4)r` `:.y=(1)/(4)r` `v=-(GM)/(x)-(Gm)/(y)` `=-G[(9m)/((3)/(4)x)+(m)/((1)/(4)r)]` `=-(Gm)/(r)[12+4]` `=(16Gm)/(r)`

9.	Calculate the angular speed of the hour hand of a clock .A. `(1)/(50)`B. `(1)/(60)`C. `(1)/(120)`D. `(1)/(720)`
Answer» Correct Answer - C `omega=(V)/(t)=(360)/(3600xx12)=(1)/(120)`

10.	When the observer moves towards the stationary source with velocity, `v_1`, the apparent frequency of emitted note is `f_1`. When the observer moves away from the source with velocity `v_1`, the apparent frequency is `f_2`. If v is the velocity of sound in air and `f_1/f_2` = 2,then `v/v_1` = ?A. 2B. 3C. 4D. 5
Answer» Correct Answer - B `F_(1)=(F[v+v_(1)])/(v),F_(2)(F[v-v_(2)])/(v)` `(F_(1))/(F_(2))=(F[v+v_(1)])/(v)xx(v)/(F[v-v_(1)])` `2=(v+v_(1))/(v-v_(1))` `2v-2v_(1)=v_(1)+v` `v=3v_(1)` `(v)/(v_(1))=3`

11.	The bob of a simple pendulum performs SHM with period T in air and with period `T_(1)` in water. Relation between T and `T_1` is (neglect friction due to water, density of the material of the bob is = `9/8xx 10^3 (kg)/m^3`, density of water = `10^3(kg)/m^3`)A. `T_(1)=3T`B. `T_(1)=2T`C. `T_(1)=T`D. `T_(1)=(T)/(2)`
Answer» Correct Answer - A `T_(1)=(T)/(sqrt(1-(p)/(p_(m))))=(T)/(1-(10^(3))/((9)/(8)xx10^(-3)))` `=(T)/(sqrt(1-(8)/(9)))=(T)/(sqrt((9-8)/(9)))=(T)/(sqrt((1)/(9)))=(T)/((1)/(3))=3T`

12.	Let M be the mass and L be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case, axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case isA. 1B. `(1)/(2)`C. `(1)/(4)`D. `(1)/(8)`
Answer» Correct Answer - B `I_(c)=(ML^(2))/(12)` `K_(c)=(L)/(sqrt(12))` `I_(e)=(ml^(2))/(3)` `K_(e)=(1)/(sqrt(3))` `(K_(c))/(K_(e))=(L)/(sqrt(12))xx(sqrt3)/(L)=(1)/(2)`.

13.	A disc of radius R and thickness R/6 has moment of inertia / about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter isA. `(I)/(5)`B. `(I)/(6)`C. `(I)/(32)`D. `(I)/(64)`
Answer» Correct Answer - A `(4pi)/(3)R_(1)^(3)=Axxt` `(4pi)/(3)R_(1)^(3)=piR^(2)(R)/(6)` `R_(1)^(3)=(1)/(8)R^(3)` `R_(1)=(1)/(2)R` `I_(1)=(2)/(5)MR_(1)^(2)=(2)/(5)M((R)/(2))^(2)` `=(2)/(5)(MR^(2))/(4)` `=(1)/(5)=(MR^(2))/(2)=(I)/(5)`

14.	Wire having tension 225 N produces six beats per second when it is tuned with a fork. When tension changes to 256 N, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will beA. 186 HzB. 225 HzC. 256 HzD. 280 Hz
Answer» Correct Answer - A `T_(1)=225N,T_(2)=256N` `n_(2)-n=6" "n_(2)gtngtn_(1)` `(n-n_(1)=6)/(n_(2)-n_(1)=12)` `(n_(2))/(n_(1))=sqrt((T_(2))/(T_(1)))=sqrt((256)/(225))=(16)/(25)` `(n_(2)-n_(1))/(n_(1))=(16-15)/(15)` `(12)/(n_(1))=(1)/(15)` `n_(1)=180Hz " "n=n_(1)+6` `n=180+6` =186 Hz