A number of identical cubical blocks of edge | vedclass

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

Question

(B) The total number of blocks is $N = n + 1$. Initially, all blocks are on the table, so their center of mass is at height $h_i = a/2$. After stackin

Vedclass · Accepted Answer

$\frac{1}{2}ma\,g\left( {{n^2} + n} \right)$

Vedclass · Answer

(B) The total number of blocks is $N = n + 1$. Initially, all blocks are on the table, so their center of mass is at height $h_i = a/2$. After stacking them into a column of height $H = (n + 1)a$, the center of mass of the column is at $h_f = H/2 = (n + 1)a/2$. The total mass of the system is $M = (n + 1)m$. The work done is equal to the change in gravitational potential energy: $W = \Delta U = M g (h_f - h_i)$. $W = (n + 1)m g \left[ \frac{(n + 1)a}{2} - \frac{a}{2} \right]$. $W = (n + 1)m g \left[ \frac{na + a - a}{2} \right] = (n + 1)m g \left( \frac{na}{2} \right)$. $W = \frac{1}{2} m a g (n^2 + n)$.

$A$ number of identical cubical blocks of edge $a$ and mass $m$ are lying on a horizontal table. The work done on the blocks in arranging them in a column of height $(n + 1)a$ on the table is

Similar Questions

Calculate the work done in rotating a vertical meter scale of mass $400 \, g$ by an angle of ${60^o}$. (in $, J$)

Potential energy of a particle varies with position $r$ as,$U = \left( \frac{\alpha}{r^4} - \frac{\beta}{r^5} \right) \text{ J}$,where $\alpha$ and $\beta$ are positive constants. The particle will be in equilibrium at $r = \dots$

If the potential energy of a particle is given by $U = A - Bx^2$,then the force is proportional to which of the following?

The decrease in the potential energy of a ball of mass $20 \,kg$ which falls from a height of $50 \,cm$ is ............ $J$.

$A$ particle moves under the influence of a force $F = -2x$ in one dimension (where $x$ is the distance of the particle from the origin). Assume that the potential energy of the particle at the origin is zero. The schematic diagram of the potential energy $U$ as a function of $x$ is given by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module