Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

1.State paralogram law of vector addition and derive magnitude and the direction of a resultant vector  
Asked by preethiprithivi05 | 21 Feb, 2023, 09:28: PM
answered-by-expert Expert Answer
Law of paralellogram of addition of two vectors states that if two vectors are represented as adjacent sides of parallelogram ,
 
then the resultant of these two vector is diagonal of parallelogram by manitude and direction.
 
Fig(1) shows two given vectors begin mathsize 14px style a with rightwards arrow on top end style and begin mathsize 14px style b with rightwards arrow on top end style. In Fig.(2), it is shown that the given vectors are adjanct sides OA and OB of parallelogram OACB.
Then the resultant vector begin mathsize 14px style a with rightwards arrow on top space plus space b with rightwards arrow on top end style is diagonal OC as shown in figure. (2)
If θ is angle between vectors  begin mathsize 14px style a with rightwards arrow on top end style and begin mathsize 14px style b with rightwards arrow on top end style, then magnitude of resultant vector begin mathsize 14px style a with rightwards arrow on top space plus space b with rightwards arrow on top end style is determined by using law of cosines as shown in fig.(3)
In fig.(3) , ΔOBC is part of parallelogram shown in fig.(2) . Magnitude of side OB is magnitude of begin mathsize 14px style b with rightwards arrow on top end style and magnitude of BC is magnitude of begin mathsize 14px style a with rightwards arrow on top end style
begin mathsize 14px style angle end styleOBC = ( 180 - θ ) , where θ is angle between vectors .
Magnitude of side OC equals to magnitude of resultant vector begin mathsize 14px style a with rightwards arrow on top space plus space b with rightwards arrow on top end style .
Magnitude of OC is determined from law of cosines as
 
begin mathsize 14px style open vertical bar a with rightwards arrow on top space plus space b with rightwards arrow on top close vertical bar squared space equals space open vertical bar a with rightwards arrow on top close vertical bar squared space plus space open vertical bar b with rightwards arrow on top close vertical bar squared space minus space 2 space open vertical bar a with rightwards arrow on top close vertical bar space space open vertical bar b with rightwards arrow on top close vertical bar space cos left parenthesis 180 minus theta right parenthesis end style
 
begin mathsize 14px style open vertical bar a with rightwards arrow on top space plus space b with rightwards arrow on top close vertical bar squared space equals space open vertical bar a with rightwards arrow on top close vertical bar squared space plus space open vertical bar b with rightwards arrow on top close vertical bar squared space plus space 2 space open vertical bar a with rightwards arrow on top close vertical bar space space open vertical bar b with rightwards arrow on top close vertical bar space cos theta end style

 
begin mathsize 14px style open vertical bar a with rightwards arrow on top space plus space b with rightwards arrow on top close vertical bar to the power of blank space equals space square root of stretchy vertical line a with rightwards arrow on top stretchy vertical line squared space plus space stretchy vertical line b with rightwards arrow on top stretchy vertical line squared space plus space 2 space stretchy vertical line a with rightwards arrow on top stretchy vertical line space space stretchy vertical line b with rightwards arrow on top stretchy vertical line space cos theta end root end style
 
Answered by Thiyagarajan K | 22 Feb, 2023, 12:12: PM
CBSE 11-science - Physics
Asked by dhanshreekansyakar | 09 Jan, 2024, 11:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by banhisikhapanda49 | 07 Nov, 2023, 10:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by preethiprithivi05 | 21 Feb, 2023, 09:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by rk274268 | 05 Aug, 2022, 01:19: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by Kattaithihaas | 24 Jul, 2022, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by kaziryan.05 | 13 Apr, 2022, 09:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by aditya000ghoderao | 19 Jan, 2022, 05:05: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by neerajchauhan000000 | 23 Sep, 2021, 03:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×