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1.

A bullet travelling horizontally looses `1//20^(th)` of its velocity while piercing a wooden plank. Then the number of such planks required to stop the bullet isA. 6B. 9C. 11D. 13

Answer» Final velocity after passing through a plank
`v=(19u)/(20)`
So, `v^(2)=u^(2)+2as,2as=-(39)/(400)u^(2)`
if bullet passes through n plands and stoopped.
`0=u^(2)+2as,u^(2)+2a(ns).`
`n=-(u^(2))/(2as)=(400)/(39)=10.3` `"So,"(n=1)`
Discussion
2.

The density of carbon dioxide gas at `0^(@)C` and at pressure `1.0 xx 10^(5) Nm^(-2)` is `1.98 kg m^(-3)`. Find the rms velocity of its molecules at `0^(@)C` and also at `30^(@)C`, assuming pressure to be constant.A. `423m//s`B. `300m//s`C. `100m//s`D. `500m//s`

Answer» `v_(ms)=sqrt((3P)/(P))=sqrt((3RT)/(M_(W))`
From I.G. equation
`P.(M)/(P)=(M)/M_(W)RT_(1)`
`M_(W)=(pRT_(1))/(P)`
`v_(ms)=sqrt((3RT_(f))/(pRT_(1))xxP`
`=sqrt(3xx10^(5)xx(273+50))/(1.98xx273)`
`=423m//s`
Discussion
3.

A particle at the end of a spring executes simple harmonic motion with a period `t_(1)` while the corresponding period for another spring is `t_(2)` if the oscillation with the two springs in series is T thenA. `T=t_(1)+t_(2)`B. `T^(2)=t_(1)^(2)+t_(2)^(2)`C. `T^(1)=t_(1)^(-1)+t_(2)^(-1)`D. `T^(2)=t_(1)^(-2)+t_(2)^(-2)`

Answer» `t_(1)=2pisqrt((m)/(k_(1)))" " ....(1),`
`t_(2)=2pisqrt((m)/(k_(2)))" " ....(2),`
when springs are in series then
`T=2pisqrt(((m)/(k_(1)k_(2)))/(k_(1)+k_(2)))=2pisqrt(m(k_(1)+k_(2)))/(k_(1)k_(2))`
squaring and adding (1) and (2) we get
`t_(1)^(2)+t_(1)^(2)=4pi^(2)(m)/k_(1)+4pi^(2)(m)/k_(2)`
`=4pi^(2)m(k_(1)+k_(2)/(k_(1)k_(2)))`
or `t_(1)^(2)+t_(2)^(2)=T^(2)`
Discussion
4.

Find the amount of work done to increase the temperature of one mole of ideal gas by `30^(@)C` .if its is expanding under the condition `V prop R^(2//3) (R = 8.31 J//mol -K):`A. `16.62J`B. `166.2J`C. `1662J`D. `1.662J`

Answer» `PV=mRT" " T`
Process `VpropT^(2//3)` or `TpropV^(3//2)`
For `PV^(x)=" constant" PVpropV^(3//2)`
`PV^(-1//2)` constant
`W=(nR)/(x-1)(dt)`
`=(1R)/(-1-(1)/(2))(-30)=(60R)/(3)=20R=166.2`
Discussion
5.

One end of a copper rod of length 1.0 m and area of cross-section `10^(-3)` is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is `92 cal//m-s-.^(@)C` and the latent heat of ice is `8xx 10^(4) cal//kg`, then the amount of ice which will melt in one minute isA. `9.2xx10^(-3)kg`B. `8xx10^(-3)kg`C. `6.9xx10^(-3)kg`D. `5.4xx10^(-3)kg`

Answer» `H=(DeltaQ)/(Deltat)=(KA(0_(H)-0_(L)))/l`
`DeltaQ=mL`
`:.(mL)/(Deltat)=(KA(0_(H)-0_(L)))/l`
`:.m=(KA(0_(H)-0_(L))Deltat)/(lL)`
`=(92xx10^(-3)xx100xx60)/(1xx80xx10^(-3))`
`=6.9xx10^(-3)kg`
Discussion
6.

The diagram (figure) shows a venturimeter, through which water is flowing the speed of water at X is 2cm/s. the speed of water at Y (taking `g=1000cm//s^(2)`) isA. `23cms^(-1)`B. `23cms^(-1)`C. `101cms^(-1)`D. `1024cms^(-1)`

Answer» `(1)/(2)pv_(1)^(2)+P_(1)=(1)/(2)pv_(2)^(2)+P_(2)`
`P_(1)-P_(2)=(1)/(2)p(v_(2)^(2)-v_(1)^(2))`
`hgd=(1)/(2)p(v_(2)^(2)-v_(1)^(2))`
`v_(2)=32m//sec.`
Discussion
7.

As per given figure to complete the circular loop what should be the radius if initial height is 5 m A. 4mB. 3mC. 2.5mD. 2m

Answer» `sqrt2gh=sqrt5gr`
`r=(2h)/(5)=(2xx5)/(5)=2m` `P=m(vdv)/(ds).v`
`underset(v)overset(2_(v))intmv^(2)dv=underset(o)overset(r)intPds`
`s=(7mv^(3))/(3P)`
Discussion
8.

In the arrangement shown in figure two equal masses (each m) hung light cords wrapped around a uniform solid cylinder of mass M and radius R. The cylinder is free to roate about a harizontal axis. If the system is released from rest then, the tension in each cord is- A. `(Mmg)/(4m+M)`B. `(Mmg)/(m+M)`C. `(Mmg)/(M+3m)`D. `(Mmg)/(2m+M)`

Answer» `mg-T=ma" "....(1)`
`2TxxR=Ialpha=MR^(2)xx(a)/(R)`
`Ma=2T`
`T=(Ma)/(2)" " ....(2)`
`mg-(Ma)/(2)=marArrmg=((Ma)/(2)+m)a`
`a=(mg)/((M)/(2)+m):.T=(mMg)/(2((M)/(2)+m))`
Discussion