A particle of mass m moving horizontally with | vedclass

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

Question

(D) $1$. Since the surface is smooth and there are no external horizontal forces acting on the system (particle + wedge),the linear momentum of the sy

Vedclass · Accepted Answer

Both $(B)$ and $(C)$.

Vedclass · Answer

(D) $1$. Since the surface is smooth and there are no external horizontal forces acting on the system (particle + wedge),the linear momentum of the system is conserved in the horizontal direction.$2$. At the maximum height $h$ relative to the wedge,the particle and the wedge move with the same horizontal velocity $V$. By conservation of momentum: $mv_0 = (m + M)V$,so $V = \frac{mv_0}{m+M}$.$3$. In the centre of mass $(COM)$ frame,the total momentum is zero. At the maximum height $h$,the relative velocity between the particle and the wedge is zero (they move together horizontally). Since the total momentum in the $COM$ frame is zero,both must be stationary with respect to the $COM$ frame.$4$. In the $COM$ frame,the total energy is the sum of the kinetic energy of the system relative to the $COM$ and the potential energy. At the maximum height $h$,the relative kinetic energy is zero,meaning all the initial kinetic energy relative to the $COM$ has been converted into potential energy $mgh_{eff}$.$5$. Thus,both statements $(B)$ and $(C)$ are correct.

Similar Questions

$A$ particle starts from the point $(0\,m, 8\,m)$ and moves with a uniform velocity of $3\, \hat{i} \,m/s$. After $5\,s$,the angular velocity of the particle about the origin will be:

$Assertion$ : If polar ice melts, days will be shorter.
$Reason$ : Moment of inertia decreases and thus angular velocity increases.

If the Earth suddenly stops rotating about its own axis,the increase in its temperature will be

Consider a sphere of mass $m$ and radius $R$ performing pure rolling motion on a rough surface with velocity $v_0$ as shown in the figure. It makes an elastic impact with a smooth wall,moves back,and eventually starts pure rolling again.

$A$ sphere rotates with an angular velocity $\omega_0$ at a temperature of $0^{\circ}C$. What will be its new angular velocity when the temperature is increased to $100^{\circ}C$? (Given: $\alpha = 2.0 \times 10^{-5} \, ^{\circ}C^{-1}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module