F1 and F2 at θ1
Fnet1=P2+Q2+P2+Q2+2(P2+Q2)cosθ1
Fnet2=P2+Q2+P2+Q2+2(P2+Q2)cosθ2
If Fnet1=3(P2+Q2)=2(P2+Q2)+2(P2+Q2)cosθ1
⇒cosθ1=2(P2+Q2)P2+Q2
⇒θ1=60∘
Fnet2=2(P2+Q2)=2(P2+Q2)+2(P2+Q2)cosθ2
⇒cosθ2=0⇒θ2=90∘
JEE Main 2021 — Physics Mechanics
Statement-I : Two forces (P+Q) and (P−Q) where P⊥Q, when act at an angle θ1 each other, the magnitude of their resultant is 3(P2+Q2), when they act at an angle θ2, the magnitude of their resultant becomes 2(P2+Q2). This is possible only when θ1<θ2.
Statement-II : In the situation given above.
θ1=60∘ and θ2=90∘
In the light of the above statement, choose the most appropriate answer from the options given below :
Held on 31 Aug 2021 · Verified 1 Jul 2026.
Statement I is false but Statement II is true.
Both Statement I and Statement II are true.
Both Statement I and Statement II are false.
Statement I is true but Statement II is false.
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8$ N/m$^2$. Area of cross-section of upper wire is $0.008$ cm$^2$ and of lower wire is $0.004$ cm$^2$. The maximum mass that can be added to pan without breaking any wire is _____ kg. (take $g = 10$ m/s$^2$) 
Given below are two statements: Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth. Statement II: The time period of revolution of the satellite is $T=2 \pi \sqrt{\frac{R_{e}}{g}}$ (for satellite very close to the earth surface), where $R_{\mathrm{e}}$ radius of earth and $g$ acceleration due to gravity. In the light of the above statements, choose the correct answer from the options given below :
From $18$ m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is _____ m. (Take $g = 10$ m/s$^2$ and neglect the air resistance)
When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height $h$. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1 \%$ each, then the height of the liquid in the tube will change by $\%$.
If $\epsilon, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :
Work through every JEE Main Mechanics PYQ, year by year.