Question -
Answer -
(a) 1 kg = 103┬аg
1 m2┬а= 104┬аcm2
1 kg m2┬аsтАУ2┬а= 1 kg ├Ч 1 m2┬а├Ч1 sтАУ2
=103┬аg ├Ч 104┬аcm2┬а├Ч1 sтАУ2┬а= 107┬аg cm2┬аsтАУ2
(b) Light year is the total distance travelled by light in oneyear.
1 ly = Speed of light ├Ч One year
= (3 ├Ч 108┬аm/s) ├Ч (365 ├Ч 24 ├Ч 60 ├Ч 60 s)
= 9.46 ├Ч 1015┬аm
(c) 1 m = 10тАУ3┬аkm
Again,1 s =
1 sтАУ1┬а= 3600 hтАУ1
1 sтАУ2┬а= (3600)2┬аhтАУ2
тИ┤3 m sтАУ2┬а= (3 ├Ч 10тАУ3┬аkm)├Ч ((3600)2┬аhтАУ2)┬а= 3.88 ├Ч 104┬аkmhтАУ2
(d) 1 N = 1 kg m sтАУ2
1 kg = 10тАУ3┬аgтАУ1
1 m3┬а= 106┬аcm3
тИ┤ 6.67 ├Ч 10тАУ11┬аN m2┬аkgтАУ2┬а=6.67 ├Ч 10тАУ11┬а├Ч (1 kg m sтАУ2) (1 m2) (1 sтАУ2)
= 6.67 ├Ч 10тАУ11┬а├Ч (1 kg ├Ч 1 m3┬а├Ч 1sтАУ2)
= 6.67 ├Ч 10тАУ11┬а├Ч (10тАУ3┬аgтАУ1)├Ч (106┬аcm3) ├Ч (1 sтАУ2)
= 6.67 ├Ч 10тАУ8┬аcm3┬аsтАУ2┬аgтАУ1