Motion in a Plane

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- d

Explanation- a scalar quantity is independent of direction hence has the same value for observers with different orientations of the axes.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b

Explanation-A = i+j

 B = i-j

 A.B=|A|B|cos $\theta$

(? +? ). (? -? ) = $\left(\sqrt[]{1+1}\right)\left(\sqrt[]{1+1}\right)$ cos $\theta$

Where $\theta$  is the angle between A and B

Cos $\theta$ = $\frac{1-0+0-1}{\sqrt[]{2\sqrt[]{2}}}$ = $\frac{0}{2}=0$

$\theta$  = 90^o

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation- given |A|=2 and |B|=4

a)|A $\times B$ |=AB cos $\theta$ = 0

so 2 $\times 4$ cos $\theta$ =0

so $\theta =90$  so it matches with ii

B) |A $\times$ B|= ABcos $\theta$ =8

2 $\times 4$ cos $\theta$ =8

So $\theta$ = 0 so it matches with option i

c) |A $\times$ B|= ABcos $\theta$ =4

so $\theta$ =60 so it matches with option iv

d) |A $\times$ B|=

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation- given |A|=2 and |B|=4

a)|A $\times B$ |=AB sin $\theta$ = 0

so 2 $\times 4$ sin $\theta$ =0

so $\theta =0$ so it matches with iv

B) |A $\times$ B|= ABsin $\theta$ =8

2 $\times 4$ sin $\theta$ =8

So $\theta$ = 90 so it matches with option iii

c) |A $\times$ B|= ABsin $\theta$ =4

so $\theta$ =30 so it matches with option i

d) |A $\times$ B|= ABsi

Explanation – here A and B vectors are joint by head and tail. So C= A+B

(a) from fig iv it is clear that c=a+b

(a) from fig iii it is clear that c+b=a so a-c=b

(b) from fig I it is clear that b=a+c so b-a =c

(c) from ii it is clear

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation – a) radius of earth =6400km= 6.4 $\times {10}^{6}m$

Time period = 1 day = 24 $\times 60\times 60$ = 86400s

Centripetal acceleration a= w²r= R(2 $\pi /T$ )²=4 $\pi$ ²R/T

= $\frac{4\times {\left(\frac{22}{7}\right)}^2\times 6.4\times {10}^6}{({24\times 60\times 60)}^2}$ = 0.034m/s²

b) time = 1yr=365 $\times 24\times 60\times 60$ days= 365=3.15 $\times {10}^{7}s$

centripetal acceleration = Rw²= $\frac{4{\pi }^{2}R}{T^2}$

^{$=\frac{4\times {\frac{22}{7}}^2\times 1.5\times {10}^{11}}{({3.15\times {10}^7)}^2}=5.97\times {10}^{-3}m/s$ 2}

$\frac{a_c}{g}=\frac{5.97\times {10}^{-3}}{9.8}=\frac{1}{1642}$

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation- when it be at position P, drops a bomb to hit a target T

Let $\theta$

Speed of the plane =720km/h = 720 $\times 5/18$ = 200m/s

Altitude of the plane P’T = 1.5km= 1500m

If bomb hits the target after time t then horizontal distance travelled by

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation – due to air resistance particle energy as well as horizontal component of velocity keep on decreasing making the fall steeper then rise. When we are neglecting air resistance path is parabola when we consider air resist

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation – the boy throws the ball at an angle of 60.

Horizontal component of velocity 4cos $\theta$ = 10cos60

=10 (1/2)

=5m/s.

so horizontal speed of the car is same, hence relative velocity of car and ball in the horizontal direction will

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation – the path of the ball observed by a boy standing on the footpath is parabolic. The horizontal speed of the ball is same as that of the car, therefore ball as well car travels equal horizontal distance, due to vertical s