Answers
x has the unit km(distance)(here)
refer class 11 ncert chapter 1 physics
each term in LHS&RHS have the same unit
bt2=km
b=km/s2
about 8 years ago
Amritha ar...
If x = at + bt2, where x is the distance travelled by the body in kilometres while t is the time in seconds, then the units of b are
over 9 years ago
Khyati des...
according to the principal of homogeneity, the dimension of each term in the equation should be equal to x.
therefore, bt^2=x
b=[x]/[t^2]
b=[LT^-2]
over 9 years ago
Sambar
x is in kms . at and bt2 should have same dims . so, kms=bt2=bs2. b=kms/s2.
about 10 years ago
Jyothi
it can be answered using the "principle of homogenity"
The dimensions of x, at, bt2 should be same.
so the dimensions of b is km/s2 (Option c)
about 10 years ago
Arashgeet ...
In this question I had to find b so b is attached to t2 in dimension + - / we should take separetly
about 10 years ago
Abhishek c...
by law of diamesion each term in equ must be equal so x=bt^2. km=b*s^2.b=km/s^2
about 10 years ago
Athul Madh...
the quantities on LHS &RHS MUST have same units
thus m=b.sec.sec
thus b=m/sec/sec
about 10 years ago
Chinmay an...
3. should be the correct answer since according to formula v=ut+0.5*a*t^2
therefore here b should be the acceleration..
about 10 years ago
Jaya Raman
simple assuming x=bt^2 as if neglecting at as we are calculating bt^2
so l=bt^2
b=lt^-2
about 10 years ago
Candyman
in addition of physical quantities only that quantities should be added which has same dimensional formula hence D.F of x=D.F of at and D.F of x=D.F of
bt2.km=b*s2 = km/s2=b
about 10 years ago
Saketh
x=ut+1/2at^2. comparing with given equation b=a,i.e.acceleration.so option 3
about 10 years ago
Ajay krish...
The units on the right hand side is same as that on the left.
b*sec^2 = km.
Therefore b = km/sec^2
about 10 years ago
Raunak aga...
we add same units, since x is displacementunit of bt2 should also be in kilometre
about 10 years ago
Shivanshu
they gave x in km so we have t in sec so when we want units of b u should verify options by which we have to get km so the option would be 3
about 10 years ago
Deeksha
the units of distance is kilometers. the units of the physical quantities should be equal to each other in an equation. therefore the units of "at" and "bt2" are kilometers. as the units of "t2" is "sec2" to make the units of "bt2" kilometers the unit of "b" should be "km/s2".
about 10 years ago
Arundutt
x=kilometers
so,at+bt2=kilometers
time should be cancelled => b=kilometers/time2
about 10 years ago
J.saikiran...
compare the dimensions of each term
as X= km
at and bt^2 has to be km now solve it
about 10 years ago
Archie Cra...
see diff it 2 times,ull get acc as b=a/2
since 2 is constant no change in dim so only consider dim of acc.
about 10 years ago
Swapnil
consider in single terms. x=at and x=bt2. This implies b=x/t2. this implies b=km/s2
about 10 years ago
Ajay sharm...
x is in a unit of distance (km)
so bt^2 is also a unit of distance. something times t2 is km => km/t2=b
about 10 years ago
Rohit Rath...
from the principle of homogenity in UNITS and DIMENsions we can equate x = bt(square) and then we can easily find the dimensions , got IT my friend ?
about 10 years ago
Amogh
differentiate the equation twice with respect to time
then you will get acceleration A=2b
km/s^2 =b
so option 3 is the answer
about 10 years ago
Venkat Pin...
according to principle of homogenity of dimensions, x shouldhave same dimension of bt^2
therefore as x is in km and t in sec
unit of b is 3.km/s^2
over 10 years ago
Gopikrishn...
dimensions of b*t2 should be km...therefore dimensions of b should be km/s2 to cancel dimesions of t2 that come in its product
over 10 years ago
Rohit
like units add up ,so at and bt^2 have same units so bt^2 has units of x ie. km
(km)=b(s)^2 so b has units km/s^2
over 10 years ago
Aniket Raw...
option 3 is correct........sum of two units will always have same units......equate units directly....this gives option 3
over 10 years ago
K. akshay ...
at+bt^2=x
therefore, dimensional formula of bt^2=[L]
b[T]^2=[L]
b=[L][T]^-2
over 10 years ago
Keerthy Sr...
oly like quantities can be added.... so bt^2 dimensions hav to be in terms of distance
over 10 years ago
Niresh
t is denoted as time
so t represents seconds
x is given as meters so the dimensional formula should be equal to'L'
so b*t squared should be equal to L so if bis km/sec squared then the total should be L
over 10 years ago
Sidhartha
According to Principle of Homogenity, every term in the equation must have same dimensions.
over 10 years ago
Srinath Go...
comparing with newton's eqn for uniformly accelerated motion (s=ut+1/2at^2) we have unit of b as unit of acceleration . i.e. km/s^2 opt(3)
over 10 years ago
Anish m m
it should be km/s sq. It is in the form of one kinematics equation. Comparing it with s=ut+1/2at sq., we can say that b should have the the units of a i.e. acceleration.
over 10 years ago
Sujit Kuma...
We can add or subtract physical quantities having sam dimensions and result obtained is also of same dimension.
Therefore, dimensionally
x = bt^2
b=x/t^2
over 10 years ago
Ritesh Aga...
km/s^2 is the answer....
b'coz as x is measured in km, bt^2 also must be measured in km......
so df of bt^2=km
b=km/t^2=km/s^2
over 10 years ago
Bsp
1)u can guess the formula i.e. S=ut + 1/2at.t
or
2)2 quantities can only be added if they have the same units so [a]=[b.t]
over 10 years ago
Sunita
s=ut+at(t/2) where u=initial velocity, t=time period,a=acceleration.
over 10 years ago
Hemanth ra...
X has unit of displacement, that is km. So, the units of 'at' and 'bt^2' must also concur with X. Hence b shouod have the unit km/s^2
over 10 years ago
Reshov sad...
because each at and bt^2 are dimensionlly equal to the x
so bt^2 = x means b = xt^-2 means km/s^2
over 10 years ago
Abhishek M...
ok so what we have here is that
x is in km
so at and bt^2 are both in km
that gives
bt^2 = km
b * t^2 = km
b= km/t^2
b= km/s^2
Enjoy :D
over 10 years ago
Projjal gu...
the answer must be in km . so bt^2 must be in km and t is sec. so if we divide with km/s^2 it becomes in km
over 10 years ago
Prithvi Kr...
we know from equations of motion (s=ut+1/2At2)it is of the form x=at bt2 so b has units of A so the units are m/s2 or km/s2
over 10 years ago
Mourya
since x has unit -metre "at" and"at2" must have unit equal to metre. therefore option 3 is correct
over 10 years ago
Tushar ran...
derivate the given equation.
take second order derivative.
u will get d2x/dt2 take units of the derive derivative ur answer is there.
over 10 years ago
Jijo Firos...
3. because x is in metres so at and bt^2 should have dimension of displacement that is [L]...THUS B IS EQUIVALENT TO ACCELERATION
over 10 years ago
Himanshu
bt^2 must have the dimmensions of distance(principle of homogenity) and hence "b" must have the dimmensions of distance/(time)^2 ==[ LT^-2]
almost 11 years ago
Abhishek
see samson by Principle of Homogenity physical quantities can be added/subtracted.This implies x=bt2 Therefore dimensions of b are M0LT-2 which is acceleration so the unit is km/s2
almost 11 years ago
Raj baldev
according to principle of homogenity dimensions of x is equals to dimensions of bt2. now it can be solve easily and answer is km/s2
almost 11 years ago
Kaushal
dimensions of t is sec and so dimensions of b should be in sec inverse
almost 11 years ago
Prajwal Na...
see......since x is in km...bt2 should also be in km so by equating bt2 with km we get the result.
about 11 years ago
Sonam
As dimension of each part is same dimension of x=dimension of bt^2 so b=x/t^2
about 11 years ago
Harshala
Comparing the given equation with the equation of motion
S=ut +(1/2)at2...
about 11 years ago
Shimon
x represents distance.
thus differentiating x gives velocity v, as
v=a+2bt
again differentiating v gives us acceleration a, as
a=2b or b=a/2
therefore unit of b is equal to unit of acceleration
here distance is in km and time in seconds, thus unit of b is km/s^2 or option 3.
about 11 years ago
Aditya
dimension of x is kilometer so the resultant of at+bt2 should also have that dimension
values having same dimensions can be added
about 11 years ago
Anjali Tek...
the unit of x is km.Now bt2 is (unit of b) multiples of t2 =km
=> (unit of b)=km/t2
=km/s2
about 11 years ago
Souvik
its km/s2 because x is distance so according to principle of homogenity all values on other side of equals should be same
about 11 years ago
Vasudha
3.km/s2 because by homogenity of principle the every term have same dimension in the algebrical expression
about 11 years ago
Chandrajit...
in order to use a equal to sign the dimensions on both side of the = sign must be same
so unit of a=km/s and that of b= kms2
about 11 years ago
Uma Pant
net units must remain of km and similar units are added ,so 'b' has units like km/sec2 and 'a' has of km/sec
about 11 years ago
Bharat Ana...
bt2 must be a dimension of distance hence it will only if b has a dimension of km/s2.
about 11 years ago
Avi Kumar
it is 3. km/s^2 because of principle of homogenity of dimensions.
That is, only quantities with same dimension (units) can be added together and can be equal. Thus dimensions of bt^2 are same as that of x.
=> units of b = (units of x) / (units of t^2) = km / s^2
over 11 years ago
James
by using dimensional analysis,
quantity of equal dimensionsare added or substracted
so x=l,
so bt2=l
b=lt(-2)
over 11 years ago
Pavan Kuma...
ans 3..........because x=distance=[L]
therefore x= bt2......t2=[t2]
b=L/t2
over 11 years ago
Ravijeet C...
x is in kilometres so at and bt must respectively be also kilometres....as t^2 is seonds^2 so to obtain kms frm the expression bt2 b must be km/s2
over 11 years ago
Darshana C...
here dimensions of x [l]
dimensions of t [T]
only similiar dimensional quantities can be added . so
bt2=L
i.e
b T2 = l1
b=L1 T-2
over 11 years ago
Dhruv hald...
choice 3 is the correct choice as only the quantities with similar dimensional formula can be added or subtracted or can be equated hence bt^2 = km
=> km/sec^2 = b
over 11 years ago
Anant
This equation is similar to the second equation of motion
so on comparing the two b is equal to acceleration.
So units are of acceleration.
about 12 years ago
Vinti sing...
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