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Properties of Matter question

2025 · Q180
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Properties of Matter question

2025 · Q180

NEETPhysicsProperties of MatterMCQ+4 / −1

Consider a water tank shown in the figure. It has one wall at x=Lx=Lx=L and can be taken to be very wide in the zzz direction. When filled with a liquid of surface tension SSS and density ρ\rhoρ, the liquid surface makes angle θ0(θ0≪1)\theta_0\left(\theta_0 \ll 1\right)θ0​(θ0​≪1) with the xxx-axis at x=Lx=Lx=L. If y(x)y(x)y(x) is the height of the surface then the equation for y(x)y(x)y(x) is:

NEET 2025 Physics - Properties of Matter Question 1 English

(take θ(x)=sin⁡θ(x)=tan⁡θ(x)=dydx,g\theta(x)=\sin \theta(x)=\tan \theta(x)=\frac{d y}{d x}, gθ(x)=sinθ(x)=tanθ(x)=dxdy​,g is the acceleration due to gravity)

  1. A
    d2ydx2=ρgs\frac{d^2 y}{d x^2}=\sqrt{\frac{\rho g}{s}}dx2d2y​=sρg​​
  2. B
    dydx=ρgsx\frac{d y}{d x}=\sqrt{\frac{\rho g}{s}} xdxdy​=sρg​​x
  3. C
    d2ydx2=ρgsx\frac{d^2 y}{d x^2}=\frac{\rho g}{s} xdx2d2y​=sρg​x
  4. D
    d2ydx2=ρgsy\frac{d^2 y}{d x^2}=\frac{\rho g}{s} ydx2d2y​=sρg​y
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