Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics-

General

Easy

Question

Two vectors $stack A with rightwards arrow on top$ and $stack B with rightwards arrow on top$ are inclined at an angle $theta$ . Now if the vectors are interchanged then the resultant turns through an angle $beta$ . Which of the following relation is true

$\tan \frac{α}{2} = {(\frac{A - B}{A + B})}^{2} \tan \frac{θ}{2}$
$\tan \frac{α}{2} = (\frac{A - B}{A + B}) \tan \frac{θ}{2}$
$\tan \frac{α}{2} = {(\frac{A - B}{A + B})}^{2} \cot \frac{θ}{2}$
$\tan \frac{α}{2} = (\frac{A - B}{A + B}) \cot \frac{θ}{2}$

The correct answer is: $tan invisible function application fraction numerator alpha over denominator 2 end fraction equals open parentheses fraction numerator A minus B over denominator A plus B end fraction close parentheses tan invisible function application fraction numerator theta over denominator 2 end fraction$

$stack A with rightwards arrow on top equals A stack A with hat on top equals B stack B with hat on top.$ let $theta$ be the angle between $stack A with rightwards arrow on top$ and $stack B with rightwards arrow on top.$
As per question,
$c o s alpha equals fraction numerator open parentheses A stack A with hat on top plus B stack B with hat on top close parentheses. left parenthesis A stack B with hat on top plus B stack A with hat on top right parenthesis over denominator open vertical bar A stack A with hat on top plus B stack B with hat on top close vertical bar open vertical bar A stack B with hat on top plus B stack A with hat on top close vertical bar end fraction$
or $c o s alpha equals fraction numerator 2 A B plus left parenthesis A to the power of 2 end exponent plus B to the power of 2 end exponent right parenthesis c o s theta over denominator open parentheses square root of A to the power of 2 end exponent plus B to the power of 2 end exponent plus 2 A B end root c o s theta close parentheses to the power of 2 end exponent end fraction$
or $2 A B plus open parentheses A to the power of 2 end exponent plus B to the power of 2 end exponent close parentheses c o s theta equals left parenthesis A to the power of 2 end exponent plus B to the power of 2 end exponent right parenthesis c o s alpha plus 2 A B c o s theta c o s alpha$
or $2 A B left parenthesis 1 minus c o s alpha c o s theta right parenthesis$
$equals open parentheses A to the power of 2 end exponent plus B to the power of 2 end exponent close parentheses left parenthesis c o s alpha minus c o s theta right parenthesis$
o $fraction numerator 2 A B over denominator A to the power of 2 end exponent plus B to the power of 2 end exponent end fraction equals fraction numerator c o s alpha minus c o s theta over denominator 1 minus c o s alpha c o s theta end fraction$
or $fraction numerator 2 A B over denominator left parenthesis A to the power of 2 end exponent plus B to the power of 2 end exponent right parenthesis end fraction equals fraction numerator c o s alpha minus c o s theta over denominator 1 minus c o s alpha c o s theta end fraction$
or $fraction numerator 2 A B plus left parenthesis A to the power of 2 end exponent plus B to the power of 2 end exponent right parenthesis over denominator open parentheses A to the power of 2 end exponent plus B to the power of 2 end exponent close parentheses minus A B end fraction$
$equals fraction numerator open parentheses c o s alpha c o s theta close parentheses plus left parenthesis 1 minus c o s alpha c o s theta right parenthesis over denominator open parentheses 1 minus c o s alpha c o s theta close parentheses plus left parenthesis c o s alpha c o s theta right parenthesis end fraction$
or $fraction numerator open parentheses A plus B close parentheses to the power of 2 end exponent over denominator open parentheses A minus B close parentheses to the power of 2 end exponent end fraction equals fraction numerator open parentheses 1 plus c o s alpha close parentheses left parenthesis 1 minus c o s theta right parenthesis over denominator open parentheses 1 plus c o s theta close parentheses left parenthesis 1 minus c o s alpha right parenthesis end fraction$
$equals fraction numerator tan to the power of 2 end exponent invisible function application theta divided by 2 over denominator tan to the power of 2 end exponent invisible function application theta divided by 2 end fraction$
or tan $fraction numerator alpha over denominator 2 end fraction equals open parentheses fraction numerator A minus B over denominator A plus B end fraction close parentheses tan invisible function application fraction numerator theta over denominator 2 end fraction$

Related Questions to study

A ball is projected with velocity $V subscript o end subscript$ at an angle of elevation $30 degree$ . Mark the correct statement

A ball is projected with velocity $V subscript o end subscript$ at an angle of elevation $30 degree$ . Mark the correct statement

Physics-General

An object moves at a constant speed along a circular path in a horizontal $X Y$ plane, with the centre at the origin. When the object is at $x equals negative 2 m$ , its velocity is $negative left parenthesis 4 m divided by s right parenthesis stack j with hat on top$ . What is the object’s acceleration when it is $y equals 2 m$

An object moves at a constant speed along a circular path in a horizontal $X Y$ plane, with the centre at the origin. When the object is at $x equals negative 2 m$ , its velocity is $negative left parenthesis 4 m divided by s right parenthesis stack j with hat on top$ . What is the object’s acceleration when it is $y equals 2 m$

Physics-General

The horizontal range of a projectile is $4 square root of 3$ times its maximum height. Its angle of projection will be

The horizontal range of a projectile is $4 square root of 3$ times its maximum height. Its angle of projection will be

Physics-General

parallel

A projectile can have the same range $R$ for two angles of projection. If $T subscript 1 end subscript$ and $blank T subscript 2 end subscript$ be the times of flights in the two cases, then the product of the two times of flights is directly proportional to

A projectile can have the same range $R$ for two angles of projection. If $T subscript 1 end subscript$ and $blank T subscript 2 end subscript$ be the times of flights in the two cases, then the product of the two times of flights is directly proportional to

Physics-General

A vector $stack A with rightwards arrow on top$ points vertically upwards and $stack B with rightwards arrow on top$ points upwards North. The vector product $stack A with rightwards arrow on top cross times blank stack B with rightwards arrow on top$ is

A vector $stack A with rightwards arrow on top$ points vertically upwards and $stack B with rightwards arrow on top$ points upwards North. The vector product $stack A with rightwards arrow on top cross times blank stack B with rightwards arrow on top$ is

Physics-General

The angle of projection of a projectile for which the horizontal range and maximum height are equal is

The angle of projection of a projectile for which the horizontal range and maximum height are equal is

Physics-General

parallel

A body can throw a stone up to a maximum height of $10 m$ . The maximum horizontal distance that the boy can throw the same stone up to will be

A body can throw a stone up to a maximum height of $10 m$ . The maximum horizontal distance that the boy can throw the same stone up to will be

Physics-General

$3 x minus 9 greater or equal than 0 space a n d space 0 less or equal than 2 x minus 4 less than 8 space t h e n space x element of$

$3 x minus 9 greater or equal than 0 space a n d space 0 less or equal than 2 x minus 4 less than 8 space t h e n space x element of$

The magnitude of magnetic induction for a current carrying toroid of uniform cross-section is

The magnitude of magnetic induction for a current carrying toroid of uniform cross-section is

Physics-General

parallel

A circular ring of diameter 20 cm has a resistance of 0.01 $capital omega$ . The charge that will flow through the ring if it is turned from a position perpendicular to a uniform magnetic field of 2.0 T to a position to the field is about

A circular ring of diameter 20 cm has a resistance of 0.01 $capital omega$ . The charge that will flow through the ring if it is turned from a position perpendicular to a uniform magnetic field of 2.0 T to a position to the field is about

Physics-General

An electric motor runs a DC source of emf 200V and draws a current of 10A. If the efficiency is 40%, then the resistance of the armature is

An electric motor runs a DC source of emf 200V and draws a current of 10A. If the efficiency is 40%, then the resistance of the armature is

Physics-General

The square root of the product of inductance and capacitance has the dimension of

The square root of the product of inductance and capacitance has the dimension of

Physics-General

parallel

The current in a $L R$ circuit builds up to 3/4^th of its steady state value in 4 $s$ . The time constant of this circuit is

The current in a $L R$ circuit builds up to 3/4^th of its steady state value in 4 $s$ . The time constant of this circuit is

Physics-General

A conducting rod of length l is moving in a transverse magnetic field of strength B with velocity v. The resistance of the rod is R. the current in the rod is

A conducting rod of length l is moving in a transverse magnetic field of strength B with velocity v. The resistance of the rod is R. the current in the rod is

Physics-General

A copper rod of length $l$ is rotated about one end perpendicular to the magnetic field $B$ with constant angular velocity $omega$ . The induced e.m.f. between the two ends is

A copper rod of length $l$ is rotated about one end perpendicular to the magnetic field $B$ with constant angular velocity $omega$ . The induced e.m.f. between the two ends is

Physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.