CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A sphere of mass $$M$$ and radius $$r$$ slips on a rough horizontal plane. At some instant it has translation velocity $${v}_{0}$$ and rotational velocity about the centre $${v}_{0}/2r$$. The translation velocity after the sphere starts pure rolling
1031213_6d547ece035243ecaebcd575956269bd.png


A
6v0/7 in forward direction
loader
B
6v0/7 in backward direction
loader
C
7v0/6 in forward direction
loader
D
7v0/6 in backward direction
loader

Solution

The correct option is A $$6{v}_{0}/7$$ in forward direction
Initially the velocity of COM of sphere is $$v_0$$ and angular velocity is $$w_i$$

When the pure rolling starts, let the velocity of COM of sphere be $$V$$ and angular velocity be $$w_f$$

Now,

$$f=Ma \implies a=\dfrac fM$$

$$v=v_0-at\implies v=v_0-\dfrac fM t$$       ..........(1)

Also,

$$\tau =I\alpha$$

$$f_r=\dfrac 25 Mr^2 \alpha \implies \alpha \dfrac{5f}{2Mr}$$

$$w_f=w_i+\alpha t$$

$$w_f=\dfrac{v_0}{2r}+\dfrac{5ft}{2Mr}\implies \dfrac 25 rw_f=\dfrac{v_0}{2}\times \dfrac 25+\dfrac{ f_t}{M}$$        ........(2)

Adding (1) and (2), we get

$$v+\dfrac 25 rw_f=\dfrac{v_0}{5}+v_0$$

Also

$$v=rw_f$$    (pure rolling)

$$\implies v=\dfrac{6v_0}{7}$$ in forward direction.


1479879_1031213_ans_20d3b3e4e1a34345805fe847ad5f26b0.png

Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image