Processing math: 23%




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6.

 Two spheres P and Q   for equal radii have densities  ρ1 and ρ2, respectively, The spheres are connected by a massless string and placed in liquids L1 and L2 of densities  σ1   and σ 2  and viscosities η1 and η2, respectively. They float in equilibrium with the sphere P  in L1  and sphere Q  in L2   and the string being taut (see figure). If  sphere  P alone in L2  has  terminal  velocity  vp  and Q alone in L1 has terminal velocity vQ, then

1032021544_p1.PNG

 


A) |VP||VQ|=η1η2

B) |VP||VQ|=η2η1

C) [V_{P}.V_{Q}&gt;0

D) V_{P}.V_{Q}&lt;0



7.

A fission  reaction is given by   23692U14054Xe+9438Sr+x+y  , where  x and y are two paricles.  Considering   23692U to be at rest, the kinetic energies of the products are denoted bt Kxe , Ksr , Kx  (2MeV) and  Ky   (2 MeV), respectively, Let the binding energies per nucleon of  23692U . 14054xe  and  9438sr be 7.5 MeV , 8.5 MeV and 8.5 MeV, respectively. Considering different vconservation laws , the correct options is/are


A) x=n,y=n , Ksr=129MeV,Kxe=86MeV

B) x=p, y=e, Ksr=129MeV,Kxe=86MeV

C) x=p, y=n, KSr=129MeV,KXe=86MeV

D) x=n,y=n, KSr=86MeV,KXe=129MeV



8.

An ideal monoatomic gas is confined ina horizontal cylinder by a spring-loaded piston  (as shown in the figure). Initially, the gas is at temperature T1,  pressure P1  and volume V1  and the spring is in its relaxed state.  The gas is then heated very slowly to temperature T2, pressure P2  and volume V2  . during this process the piston moves out  by a distance of x, Ignoring the friction  between the piston and the cylinder, the correct statements is/are

932021227_p13.JPG


A) If V_{2}=2V_{1} and T_{2}=3T_{1} , then the energy stored in the spring is \frac{1}{4}p_{1}V_{1}

B) If V_{2}=2V_{1} and T_{2}=3T_{1} , then the change in internal energy 3p_{1}V_{1}

C) If V_{2}=3V_{1} and T_{2}=4T_{1}, then the work done by the gas \frac{7}{3}p_{1}V_{1}

D) If V_{2}=3V_{1} and T_{2}=4T_{1}, then the heat supplied to the gas is \frac{17}{6}p_{1}V_{1}



9.

 A parallel plate capacitor having plates of area S and plate separation d, has capacitance  C1   in air. When two dielectrics of different relative permittivities (ε1= 2 and ε2  =4) are introduced between the two plates as shown in the figure, the capacitance becomes C2. The ratio   \frac{C_{2}}{C_{1}}  is

932021363_p10.JPG


A) \frac{6}{5}

B) \frac{5}{3}

C) \frac{7}{5}

D) \frac{7}{3}



10.

 A spherical  body of radius R consists  of a fluid  of constant density and is in equilibrium  under  its own gravity . If  P(r)  is the pressure  at r(r<R) , then  the correct options  is /are


A) P(r=0)=0

B) \frac{P(r=\frac{3R}{4})}{P(r=\frac{2R}{3})}=\frac{63}{80}

C) \frac{P(r=\frac{3R}{5})}{P(r=\frac{2R}{5})}=\frac{16}{21}

D) \frac{P(r=\frac{R}{2})}{P(r=\frac{R}{3})}=\frac{20}{27}



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