The figure below shows the top view of a hollow cylindrical room having a frictionless floor. A block of mass m is projected with a speed v , on the smooth horizontal floor, along the wall of the room. The average normal force exerted by the cylindrical walls, on the block, during its motion from A to B is

Question

The figure below shows the top view of a hollow cylindrical room having a frictionless floor. A block of mass m is projected with a speed v , on the smooth horizontal floor, along the wall of the room. The average normal force exerted by the cylindrical walls, on the block, during its motion from A to B is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-q5a25wjkhgvm.png" /> (A) (m v2/R) (B) (m v2/π R) (C) (2 m v2/R) (D) (2 m v2/π R)

Tardigrade Admin · Accepted Answer

The change in momentum of the block from

A

to

B

is

∣ Δ p ∣ = 2 m v

The time it takes to move from

A

to

B

is

Δ t = \frac{π R}{v}

The average force exerted by the wall on the block is

F_{a vg} = \frac{∣ Δ p ∣}{Δ t} = \frac{2 m v ^{2}}{π R}

$\frac{m v ^{2}}{R}$

$\frac{m v ^{2}}{π R}$

$\frac{2 m v ^{2}}{R}$

$\frac{2 m v ^{2}}{π R}$

The change in momentum of the block from $A$ to $B$ is
$∣ Δ p ∣ = 2 m v$
The time it takes to move from $A$ to $B$ is
$Δ t = \frac{π R}{v}$
The average force exerted by the wall on the block is
$F_{a vg} = \frac{∣ Δ p ∣}{Δ t} = \frac{2 m v ^{2}}{π R}$

Rmv2​

πRmv2​

R2mv2​

πR2mv2​

The change in momentum of the block from A to B is ∣Δp∣=2mv The time it takes to move from A to B is Δt=vπR​ The average force exerted by the wall on the block is Favg​=Δt∣Δp∣​=πR2mv2​

$\frac{m v ^{2}}{R}$

$\frac{m v ^{2}}{π R}$

$\frac{2 m v ^{2}}{R}$

$\frac{2 m v ^{2}}{π R}$

The change in momentum of the block from $A$ to $B$ is
$∣ Δ p ∣ = 2 m v$
The time it takes to move from $A$ to $B$ is
$Δ t = \frac{π R}{v}$
The average force exerted by the wall on the block is
$F_{a vg} = \frac{∣ Δ p ∣}{Δ t} = \frac{2 m v ^{2}}{π R}$