A particle of mass 10 text{ g} moves along a | vedclass

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

Question

(C) Given: Mass $m = 10 	ext{ g} = 10^{-2} 	ext{ kg}$, Radius $r = 6.4 	ext{ cm} = 6.4 	imes 10^{-2} 	ext{ m}$, Kinetic Energy $K = 8 	imes 10^{

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(C) Given: Mass $m = 10 	ext{ g} = 10^{-2} 	ext{ kg}$, Radius $r = 6.4 	ext{ cm} = 6.4 	imes 10^{-2} 	ext{ m}$, Kinetic Energy $K = 8 	imes 10^{-4} 	ext{ J}$.Since the particle starts from rest, its initial velocity $u = 0$.The distance covered in two revolutions is $s = 2 	imes (2 \pi r) = 4 \pi r$.Using the work-energy theorem, the work done by the tangential force $F_t$ equals the change in kinetic energy:$W = F_t \cdot s = \Delta K$Since $F_t = m a_t$, we have:$m a_t \cdot (4 \pi r) = K - 0$$a_t = \frac{K}{m \cdot 4 \pi r}$Substituting the values:$a_t = \frac{8 	imes 10^{-4} 	ext{ J}}{10^{-2} 	ext{ kg} 	imes 4 	imes 3.14 	imes 6.4 	imes 10^{-2} 	ext{ m}}$$a_t = \frac{8 	imes 10^{-4}}{25.6 \pi 	imes 10^{-4}} = \frac{8}{25.6 	imes 3.14} \approx 0.1 	ext{ m/s}^2$.

Similar Questions

$A$ clock has $75 \ cm$ and $60 \ cm$ long second hand and minute hand respectively. In $30$ minutes duration,the tip of the second hand will travel $x$ distance more than the tip of the minute hand. The value of $x$ in meters is nearly (Take $\pi = 3.14$):

The angular speed of the wheel of a vehicle is increased from $360 \; rpm$ to $1200 \; rpm$ in $14 \; s$. Its angular acceleration is,

$A$ wheel rotating at an angular velocity of $1200 \ rpm$ is slowed down at a constant angular acceleration of $4 \ rad \ s^{-2}$. How many revolutions will the wheel make before coming to rest?

The wheel of a car is rotating at the rate of $1200$ revolutions per minute. On pressing the accelerator for $10 \ s$,it starts rotating at $4500$ revolutions per minute. The angular acceleration of the wheel is:

$A$ wheel,initially at rest,is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta _1}$ in the first $1 \ s$ and through an additional angle ${\theta _2}$ in the next $1 \ s$. The ratio $\frac{{\theta _2}}{{\theta _1}}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module