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The distancebetween plates of a parallel plate capacitor is 5d. The positively charged plate is at x 0 and negatively charged plate is at x= 5d. Two slabs one of conductor andthe other of a dielectric of same thickness d are inserted between the plates as shown in figure. Potential (V) versus distance (x) graph will be 0 d 2d 3d 4d 5d

O d 2d 3d 4d 5d O d 2d 3d 4d 5d 0 d.2d 3d 4d 5d 0 d 2d 3d 4d 5d

Since electric field E (slope of V-x graph) and E inside a conductor O slope of V-x graph between x = d to x = 2d should be zero. also E in air > E in dielectric .. Slope in airl>Islope in dielectricl option (b) satisfies all conditions.

The frequency of a sonometer wire is u, but when the weights producing the tensions are completely immersed in water the frequency becomes u/2 and on immersing the weights in a certain liquid the frequency becomes u/3. The specific gravity of the liquid is 16 9 15 12 32 (d) 27 4 3

Since frequency uoc VT Where T is tension in sonometer wire 0 Vpg air air water

0 or or 2_ 4. Similarly in second case 4 3 VW 4 4 3 Pw

PL Here specific gravity of the liquid s VW 4 4 3s 36 27s 4 32 27 9= s=

A particle moves in the x-y plane under the influence of a force such that its linear momentum is p(t) A[i cos(kt) -jsin(kt) where A and k are constants. The angle between the force and the momentum is (a) 0 (b) 30 (c) 45 (d) 90

Here, p(t) = Alicos(kt)-1 sin(kt)] . .. (i) F- Akl-isin(kt)-jcos(kt)] (i) dt From equation (i) and (ii) Since | Fland |pl are not equal to zero. cos 0. 900.