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Class 10 Class 12

કણોના તંત્રનુ ડાઇનેમિક્સ

2 kg નું એક પક્ષી $open parentheses 2 space i with hat on top space plus space 4 space j with hat on top close parentheses$ m/s ના અચળ વેગથી તથા 3 kg નું બીજું પક્ષી $open parentheses 2 space i with hat on top space plus space 6 space j with hat on top close parentheses$ m/s થી ઊડતાં હોય, તો બંને પક્ષી વડે બનતાં તંત્રના દ્રવ્યમાન-કેન્દ્રનો વેગ...... m/s હોય ?

$open parentheses 2 space i with hat on top space plus space 5.2 space j with hat on top close parentheses$
$2 space i with hat on top space plus space 2 space j with hat on top$
$2 space i with hat on top space minus space 2 space j with hat on top$
$10 space i with hat on top space plus space 10 space j with hat on top$

જો 't' સમયે કોઈ પથ્થરનું વેગમાન $open square brackets open parentheses 0.5 space k g space m divided by s squared close parentheses t to the power of 2 space end exponent plus space open parentheses 3.0 space k g space m divided by s close parentheses close square brackets i with hat on top space plus space open square brackets 1.5 space k g space m divided by s squared close square brackets t space j with hat on top space space right square bracket$ હોય, તો તેના પર લાગતું બળ કેટલું હોય ?

$open parentheses t space i with hat on top space plus space 1.5 space j with hat on top close parentheses space N$
$open parentheses 0.5 t i with hat on top space plus space 1.5 j with hat on top close parentheses space N$
$open square brackets open parentheses 0.5 t space plus space 3 close parentheses i with hat on top space plus space 1.5 space j with hat on top close square brackets space N$
$open parentheses 0.5 space i with hat on top space plus space 1.5 j with hat on top close parentheses space N$

2400 kgની એક બસ સીધા રસ્તા પર્ 60 km/hની ઝડપથી જાય છે. બસની પાછળ 1600 kgની એક કાર 80 km/h ની ઝડપથી આવી રહી છે. બંને વાહનોનુ દ્રવ્યમાન-કેન્દ્ર કેટલી ઝડપથી ગતિ કરતું હશે ?

70 km/h
75 km/h
72 km/h
68 km/h

ધારો કે તમારું દ્રવ્યમાન 50 kg છે. તમારે કેટલી ઝડપથી દોડવું પડે કે જેથી તમારું રેખીય વેગમાન 20 km/h ની ઝડપથી સીધા રસ્તા પર ગતિ કરતા 100 kg સાઇકલ સવાર જેટલું થાય ?

40m/s
11.11 m/s
20 km/h
10 km/h

0.100 gનું એક પીંછું $open parentheses negative 0.05 space j with hat on top close parentheses space m divided by s$ ના વેગથી નીચે પડે છે, નીચેથી તેના પર ફુંક મારતાં તેનો વેગ $open parentheses 0.20 space i with hat on top space plus space 0.15 space j with hat on top close parentheses space m divided by s$ થાય છે, તો તેના વેગમાનમાં થતો ફેરફાર.......... kg m/s હશે.

$2 cross times 10 to the power of negative 2 end exponent space i with hat on top space plus space 2 cross times 10 to the power of negative 2 end exponent space j with hat on top$
$2 cross times 10 to the power of negative 5 end exponent space i with hat on top space plus space 2 cross times 10 to the power of negative 5 end exponent space j with hat on top$
$2 cross times 10 to the power of negative 2 end exponent space i with hat on top space plus space 1 cross times 10 to the power of negative 2 end exponent space j with hat on top$
$2 cross times 10 to the power of negative 2 end exponent space i with hat on top space minus space 2 cross times 10 to the power of negative 2 space end exponent space j with hat on top$

2 cross times 10 to the power of negative 5 end exponent space i with hat on top space plus space 2 cross times 10 to the power of negative 5 end exponent space j with hat on top

Tips: -

પ્રારંભિક વેગમાન $stack P subscript 1 with rightwards arrow on top$

$equals space m stack v subscript 1 with rightwards arrow on top equals space 0.1 space cross times space 10 to the power of negative 3 space end exponent open parentheses negative 0.05 space j with hat on top close parentheses equals space minus 0.5 space cross times space 10 to the power of negative 5 end exponent space j with hat on top$

અંતિમ વેગમાન $stack P subscript 2 with rightwards arrow on top$

$equals space 0.1 space cross times 10 to the power of negative 3 space end exponent open parentheses 0.2 space i with hat on top space plus space 0.15 space j with hat on top close parentheses equals space 2 space cross times space 10 to the power of negative 5 space end exponent i with hat on top space plus space 1.5 space cross times space 10 to the power of negative 5 end exponent space j with hat on top$

વેગમાનમાં ફેરફાર $triangle space P with rightwards arrow on top$

$equals space stack P subscript 2 with rightwards arrow on top space minus space stack P subscript 1 with rightwards arrow on top equals open parentheses 2 space cross times space 10 to the power of negative 5 space end exponent i with hat on top space plus space 1.5 space cross times space 10 to the power of negative 5 end exponent space j with hat on top close parentheses space minus space open parentheses negative 0.5 space cross times space 10 to the power of negative 5 end exponent space j with hat on top close parentheses equals space 2 space cross times space 10 to the power of negative 5 end exponent space i with hat on top space plus space 2 space cross times space 10 to the power of negative 5 end exponent space j with hat on top space k g space m divided by s$

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કણોના તંત્રનુ ડાઇનેમિક્સ

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