1
COMEDK 2024 Morning Shift
+1
-0

If potential (in volt) in a region is expressed as $$\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})=6 \mathrm{xy}-\mathrm{y}+2 \mathrm{yz}$$, the electric field (in $$N C^{-1}$$) at point $$(1,0,1)$$ is

A
$$\mathrm{-7 j}$$
B
$$+7 \mathrm{j}$$
C
$$\mathrm{-6 i+7 j}$$
D
$$\mathrm{6 i-7 j}$$
2
COMEDK 2024 Morning Shift
+1
-0

Five charges, '$$q$$' each are placed at the comers of a regular pentagon of side '$$a$$' as shown in figure. First, charge from '$$A$$' is removed with other charges intact, then charge at '$$A$$' is replaced with an equal opposite charge. The ratio of magnitudes of electric fields at $$\mathrm{O}$$, without charge at $$A$$ and that with equal and opposite charge at $$A$$ is

A
4 : 1
B
2 : 1
C
1 : 4
D
1 : 2
3
COMEDK 2024 Morning Shift
+1
-0

Two charges '$$-q$$' each are fixed, separated by distance '$$2 d$$'. A third charge '$$q$$' of mass '$$m$$' placed at the mid-point is displaced slightly by '$$x$$' $$(x< < d)$$ perpendicular to the line joining the two fixed charges as shown in Fig. The time period of oscillation of '$$q$$' will be

A
$$\mathrm{T}=\sqrt{\frac{8 \varepsilon_0 \mathrm{~m} \pi^2 \mathrm{~d}^3}{\mathrm{q}^2}}$$
B
$$\mathrm{T}=\sqrt{\frac{8 \varepsilon_0 \mathrm{~m} \pi^3 \mathrm{~d}^3}{\mathrm{q}^3}}$$
C
$$\mathrm{T}=\sqrt{\frac{4 \varepsilon_0 \mathrm{~m} \pi^3 \mathrm{~d}^3}{\mathrm{q}^2}}$$
D
$$\mathrm{T}=\sqrt{\frac{8 \varepsilon_0 \mathrm{~m} \pi^3 \mathrm{~d}^3}{\mathrm{q}^2}}$$
4
COMEDK 2024 Morning Shift
+1
-0

Two metal spheres, one of radius $$\frac{R}{2}$$ and the other of radius $$2 \mathrm{R}$$ respectively have the same surface charge density They are brought in contact and separated. The ratio of their new surface charge densities is

A
$$2: 1$$
B
$$4: 1$$
C
$$1: 4$$
D
$$1: 2$$
EXAM MAP
Medical
NEET