Physics NCERT Exemplar Solutions Class 11th Chapter Four

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

B $*A$ +B $*B+B*C$ =0

B $*A+0+B*C=0$

B $*A=-B*C$

A $*B=B*C$

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

It cannot be zero

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

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

(d) if c²= A²+B², then angle between A and B is 90⁰

(A $*B$ ).C= (AB sin90⁰X).C=AB (X.C)

= ABC cos90⁰= 0

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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 treated as vector.

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

So u²= 980

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

So u= 14 $*2.23$ = 31.304m/s

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

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

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 component q will be negative.

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.