Motion in a Plane

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- a,b,c

Explanation – H= $\frac{u^2{sin}^2\theta }{2g}$

H₁=V_o²sin^{2 $\theta$} ₁/2g  , H₂=V_o²sin^{2 $\theta$} ₂/2g

H₁>H₂

V_o²sin^{2 $\theta$} ₁/2g= V_o²sin^{2 $\theta$} ₂/2g

Sin^{2 $\theta$} ₁>sin^{2 $\theta$} ₂

Sin^{2 $\theta$} ₁ – sin² $\theta$ ₂>0

(Sin $\theta$ ₁ – sin $\theta$ ₂)( Sin $\theta$ ₁ + sin $\theta$ ₂)>0

Sin $\theta$ ₁>sin $\theta$ ₂ or ₁ >₂

T= $\frac{2usin\theta }{g}=\frac{2v_{o}sin\theta }{g}$

T₁= $\frac{2v_{o}sin{\vartheta }_1}{g}$   , T₂= $\frac{2v_{o}sin{\vartheta }_2}{g}$

T₁> T₂

R=

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- a, b

Explanation - |A+B|= |A|or |A+B|²=|A|²

|A|² +|B|²+2|A|B|cos $\theta$ = |A|²

|B| (|B|+2|A|cos $\theta$ )= 0

|B|=0 or |B|+2|A|cos $\theta$ =0

Cos $\theta$ = $\frac{-\left|B\right|}{2\left|A\right|}$

If A and B are antiparallel then $\theta$ =180

-1= $\frac{\left|B\right|}{2\left|A\right|}=\left|B\right|=2\left|A\right|$

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b, d

Explanation – given A+B+C = 0

B $\times \left(A+B+C\right)=B\times 0=0$

B $\times A$ +B $\times B+B\times C$ =0

B $\times A+0+B\times C=0$

B $\times A=-B\times C$

A $\times B=B\times C$

(A $\times B$ ) $\times C=\left(B\times C\right)\times C$

It cannot be zero

(b) (A $\times B$ ).C= (B $\times AC$ ).C=0 . if b|C then B $\times C$ =0 then (B $\times C$ ) $\times C=0$

(c) (A $\times B$ )=X=ABsin $\theta X$ . The direction of X is perpendicular to the plane containing A and B

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer-b, d

Explanation- as given motion is two-dimensional motion and given that instantaneous speed v_o is positive constant. Acceleration is rate of change of velocity. hence it will also be in the plane of motion.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- d

Explanation – speed = total distance travelled /time taken

Total distance travelled = path length

= speed $*$ time

We should be very careful with the fact, that speed is related with total distance covered not with displacement.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b

Explanation – we know that impulse J= f. $?t$ = $?p$ , where F is force . $?t$  is time duration and $?p$  is change in momentum. As $?p$ is a vector quantity, hence impulse is also a vector quantity. Sometimes area can also be tr

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- c

Explanation - we know that $\theta$ =15⁰ and R= 50m

Range, R= $\frac{u^{2}sin2\theta }{g}$

50 = $\frac{u^{2}sin2\times 15}{g}$

So u²= 980

So u = $\sqrt[]{980}=7\times 2\times \sqrt[]{5}$ m/s

So u= 14 $\times 2.23$ = 31.304m/s

$\theta$ = 45⁰, R= $\frac{u^{2}sin2\left(45\right)}{9.8}=\frac{u^2}{g}$

R= $\frac{({14\sqrt[]{5)}}^2}{g}$ = $\frac{14\times 14\times 5}{9.8}$ = $100m$

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b

Explanation – ler r makes an angle $?$ with positive x axis component if r along x-axis.

So  r_x= |r|cos $?$

(r_x)_maximum= |r| (cos $?$ )_maximum

= |r|cos $0$ = r

$?$ =0⁰

R is along positive x-axis.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b 

Explanation – u= a? + b? as u in the first quadrant, hence both components a and b will be positive. For v= p? + q? , as it is positive x direction and located downward hence x component p will be positive and y compon