Column-I (Angle of projection)Column-IIA. the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a projectile,the kinetic energy at the highest point is $K_h = \frac{1}{2}m(u \cos 	heta)^2$ and initial kinetic energy is $K_i = \frac{1}{2}

Vedclass · Accepted Answer

$A-4, B-1, C-3, D-2$

Vedclass · Answer

(C) For a projectile,the kinetic energy at the highest point is $K_h = \frac{1}{2}m(u \cos 	heta)^2$ and initial kinetic energy is $K_i = \frac{1}{2}mu^2$. Thus,$\frac{K_h}{K_i} = \cos^2 	heta$.For $A: 	heta = 45^{\circ}, \frac{K_h}{K_i} = \cos^2(45^{\circ}) = \frac{1}{2}$. (None match directly,let's evaluate $\frac{R}{H} = 4 \cot 	heta$)For $A: 	heta = 45^{\circ}, \frac{R}{H} = 4 \cot(45^{\circ}) = 4$. So $A-4$.For $B: 	heta = 60^{\circ}, \frac{K_h}{K_i} = \cos^2(60^{\circ}) = \frac{1}{4}$. So $B-1$.For $C: 	heta = 30^{\circ}, \frac{R}{H} = 4 \cot(30^{\circ}) = 4\sqrt{3}$. So $C-3$.For $D: 	heta = 	an^{-1}(4), \frac{gT^2}{R} = 2 	an 	heta = 2(4) = 8$. So $D-2$.Matching: $A-4, B-1, C-3, D-2$.

Column-$I$ (Angle of projection)	Column-$II$
$A. \theta = 45^{\circ}$	$1. \frac{K_h}{K_i} = \frac{1}{4}$
$B. \theta = 60^{\circ}$	$2. \frac{gT^2}{R} = 8$
$C. \theta = 30^{\circ}$	$3. \frac{R}{H} = 4\sqrt{3}$
$D. \theta = \tan^{-1}(4)$	$4. \frac{R}{H} = 4$

Column $I$	Column $II$
$(A)$ $u_x$ is doubled, $u_y$ is halved	$(p)$ $H$ will remain unchanged
$(B)$ $u_y$ is doubled, $u_x$ is halved	$(q)$ $R$ will remain unchanged
$(C)$ $u_x$ and $u_y$ both are doubled	$(r)$ $R$ will become four times
$(D)$ Only $u_y$ is doubled	$(s)$ $H$ will become four times

Similar Questions

$A$ particle is moving in a circle of radius $R$ with constant speed $V$. The magnitude of average acceleration after half revolution is

$A$ projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m/s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\,m/s$.

$A$ car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take the same time to complete the circles,the ratio of their angular speeds and linear speeds will be .........

$A$ stone thrown with velocity $u$ at angles $\theta$ and $(90^{\circ}-\theta)$ with the horizontal reaches maximum heights $H_1$ and $H_2$ respectively. Its horizontal range is

Vedclass Test Series

Exam Paper Generator

Online Exam Module