# National Science Olympiad Model Paper 2 Questions and Answers Part 14

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Q. 5. A body is moving in a circular path with acceleration ‘a’ . If its velocity gets four times, find the ratio of acceleration after and before the change

A) 1: 16

B) 16: 1

C) 1: 4

D) 4: 1

Explanation:

When an object moves in circular path with constant speed then it acceleration is given as,

Condition first; Speed is 4 times increases then acceleration is given as,

Ratio of final to initial acceleration will be

= = 16: 1.

Q. 6. In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4 m just after the system is released from rest is (θ = sin-13/5)

A) downwards

B) upwards

C) upwards

D) downwards

Explanation

The Free body diagram of blocks is as shown From Newton՚s second law

… (i)

and … (ii)

= 4/5 and from constraint we get

… (iii)

Solving eq. (i) , (ii) and (iii) We get acceleration of block of mass 4m,

Downwards.

Q. 7. Two bodies of mass 5 kg and 8 kg are suspended at the ends of mass-less string passing over a frictionless pulley. The acceleration of the system is (g = 9.8m/s2)

A) 4.9m/s2

B) 2.26m/s2

C) 1.4m/s2

D) 9.5m/s2

Explanation:

Acceleration =

= = 2.26

Q. 8. A bullet of mass 10 g is shot from a gun of mass 5 kg. The muzzle velocity of the bullet is 800 m/s. The recoil velocity of the gun is

A) 1.6 m/s

B) 1600 m/s

C) 1 m/s

D) Data is insufficient

Explanation:

Momentum is a vector quantity, and therefore we need to use vector addition when summing together the momentum of the multiple bodies which make up a system.

Consider a system of two similar objects moving away from each other in opposite directions with equal speed and that the oppositely-directed vectors cancel out, so the momentum of the system as a whole is zero, even though both objects are moving.

.

By the conservation of linear momentum,

Let mass and velocity of bullet be and mass and velocity of gun is so

By the formula

m/s

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