Question

7
A particle of mass m begins to slide
down a fixed smooth sphere from the
top. What is its tangential acceleration
when it breaks off the sphere?
O
29
3
—
5g
co​

Answer 1

Answer:

ANSWER

If a particle starts from the top,the speed of the particle will be given by energy conservation law.It is given as

change in the potential energy = gain in kinetic energy

mgR(1−cosθ)=

2

1

mv

2

from force equation now

since it break off at this position so normal force will be zero

mgcosθ=

R

mv

2

now we will use the value from above two equations

mgcosθ=2mg×(1−cosθ)

by solving above equation

cosθ=

3

2

now for tangential acceleration as we know that

a

t

=

m

F

m

a

t

=

m

mgsinθ

a

t

=gsinθ

from above equation

sinθ=

3

5

so tangential acceleration will be

a

t

=

3

5

g

a

t

=7.45

s

2

m

Answer 2

Answer:

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