The magnitudes of four pairs of displacement vectors are given. Which pairs of displacement vectors
cannot be added to give a resultant vector of magnitude 4 cm ?
(A) 2 cm, 3 cm (B) 1 cm, 3 cm (C) 1 cm, 5 cm (D) 1 cm, 7 cm
ThemagnitudeRoftheresultantoftwovectorsAandBdependsuponthemagnitudesofAandBandtheangleθbetweenthemandisgivenbyR2=A2+B2+2ABcosθwhenθ=0,RismaximumgivenbyR2max=A+Bwhenθ=180∘,RisminimumgivenbyRmin2=A2+B2−2ABor,Rmin=A−BThusthemagnitudeofresultantwillliebetweenA−BandA+B,.
Now,Oncheckoption(D)∣A−B∣=∣1−7∣=6∣A+B∣=∣1+7∣=8So,6≤R≤8∴R=4Hence,theoptionDisthecorrectanswer.
Now,Oncheckoption(D)∣A−B∣=∣1−7∣=6∣A+B∣=∣1+7∣=8So,6≤R≤8∴R=4Hence,theoptionDisthecorrectanswer.
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Similar questions
θbetweenthemandisgivenby
R
2
=A
2
+B
2
+2ABcosθ
whenθ=0,Rismaximumgivenby
R
2
max
=A+B
whenθ=180
∘
,Risminimumgivenby
R
min
2
=A
2
+B
2
−2AB
or,
R
min
=A−B
ThusthemagnitudeofresultantwillliebetweenA−BandA+B,
.
Now,
Oncheckoption(D)
∣A−B∣=∣1−7∣=6
∣A+B∣=∣1+7∣=8
So,6≤R≤8∴R
=4
Hence,theoptionDisthecorrectanswer.