A pendulum consists of a bob of mass m=0.1 k | vedclass

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

Question

(D) The angular momentum $J$ about the point of suspension is given by $J = r_{\perp} 	imes p$,where $r_{\perp}$ is the perpendicular distance from t

Vedclass · Accepted Answer

$0.18, 0.16$

Vedclass · Answer

(D) The angular momentum $J$ about the point of suspension is given by $J = r_{\perp} 	imes p$,where $r_{\perp}$ is the perpendicular distance from the pivot to the line of action of the impulse. Here,$r_{\perp} = H = 0.9 \ m$ and $p = P = 0.2 \ kg \cdot m/s$. Thus,$J = 0.9 	imes 0.2 = 0.18 \ kg \cdot m^2/s$.When the string becomes taut,the velocity component along the string is lost due to the impulsive tension. The bob is at an angle $	heta$ such that $\cos 	heta = H/L = 0.9/1.0 = 0.9$. The velocity of the bob just before the string becomes taut is $v = P/m = 0.2/0.1 = 2 \ m/s$. The component of velocity perpendicular to the string is $v_{\perp} = v \cos 	heta = 2 	imes 0.9 = 1.8 \ m/s$. The kinetic energy just after the lift-off is $K = \frac{1}{2} m v_{\perp}^2 = \frac{1}{2} 	imes 0.1 	imes (1.8)^2 = 0.05 	imes 3.24 = 0.162 \ J$. Rounding to two decimal places,$K \approx 0.16 \ J$.

Similar Questions

$A$ uniform rod $AB$ of mass $m$ and length $\ell$ is at rest on a smooth horizontal surface. An impulse $P$ is applied to the end $B$ perpendicular to the rod. The time taken by the rod to turn through a right angle is

$A$ rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical,its lower half separates without exerting any reaction at the breaking point. Then the maximum angle '$\theta$' made by the hinged upper half with the vertical is ......... $^o$.

$A$ thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$, the kinetic energy of the system is (neglect friction):

Vedclass Test Series

Exam Paper Generator

Online Exam Module