**Physics mcq questions based on mass,displacement,position.**

1.

A 50 gramme bullet traveling at 182 m/s buries itself in a 5.4 kg pendulum hanging on

a 2.06 m length of string, which makes the pendulum swing upward in an arc.

Determine the horizontal component of the displacement of the pendulum.

A) 0.752m

B) 1.046 m

C) 1376.598

D) 0.511 m

E) 0.057 m

Answer:

conservation of momentum

m1v1 = (m1+m2)v2

Where

m1 = mass of bullet

m2 = mass of pendulum

v1 = bullet velocity

we solve for v2, which is the velocity

of the pendulum after the bullet strikes

v2 = (m1v1)/(m2+m1)

= (.05kg)(182)/(5.4+.05)

= 9.1/5.45

= 1.669

V=1.29 m/s

So then we use conservation of energy,

to find the max height the pendulum can rise.

mgh = ½mv²

where m cancels out

g = 9.8 m/s²

v = v2 = 1.66 m/s

we want to solve for h

h = ½v²/g

h = ½(1.66)/(9.8)

h = .084 m

so now that we have the vertical displacement,

we can use the length of the string to

find the horizontal displacement.

The horizontal displacement is given by

x = [L² – (L – h)²]

where

L = length of string = 2.06 m

h = .140 m

x = [2.06² – (2.06 – .084)²]

x = [2.66² – 2.07²]

x = 1.157

x = 1.046 m

2.

You are trying to balance a tray of dishes to make it easy to carry. At one end of the 0.8m

tray are four plates with total mass 1.4kg with their centers of mass exactly above the left

edge of the tray. How far from the left edge should you place a 2.1kg jug of milk so that

the centre of mass of the system is at the centre of the tray?

A) 0.58 m

B) 0.67 m

C) 0.72 m

D) 0.53 m

E) 0.78 m

Answer:

Let the Jug is kept at a meter from the center of the tray, Thus by taking the

momentum of at the center of the tray:-

=>1.4 x 0.4 = a x 2.1

=>a = 0.4/2.1 = 0.26 m

=>The distance from the left edge = 0.40 + 0.26 = 0.666 m

=0.67m (B) is the answer

3.

A person falls flat on their back on some slippery ice and is unconscious for a second. The

horizontal position of their legs torso and head from their feet is given by 0.41m, 1.11m

and 1.8m respectively and their weights are 30kg 50kg and 10kg. They try to sit up on the

ice which is so slippery they are not able to move their horizontal centre of mass. The new

positions of their legs, torso and head from their feet are 0.23m, 0.56m and 0.8m. What is

the change in position of the person’s feet?

all you have to do is find the horizontal center of mass(X) two different times

A) 0.39 B) 0.48 C) 0.62 D) 0.72

Answer:

use this equation (center of mass equation)

X=(mass1*position1)+(mass2*position2)+

(mass3*position3) / (mass 1+2+3)

now find X using the numbers above ( masses are the 30,50,10) and their respective

positions (.41,1.11,1.18)

after u find X

find X again, this time substitute the positions values with the new set (.23,.56,.8)

after u get these two X values, basically u have found two different center of masses for

the person, so by subtracting these two values u should get his change in position

u should get .62 as your answer(C)

A person falls flat on their back on some slippery ice and is unconscious for a second.

The horizontal position of their legs torso and head from their feet is given by 0.31m,

1.39m and 1.65m respectively and their weights are 30kg 50kg and 10kg. They try to

sit up on the ice which is so slippery they are not able to move their horizontal centre of

mass. The new positions of their legs, torso and head from their feet are 0.2m, 0.57m

and 0.78m. What is the change in position of the person’s feet?

A) 0.76

B) 0.43

C) 0.59

D) 0.83

all you have to do is find the horizontal center of mass(X) two different times

use this equation (center of mass equation)

X=(mass1*position1)+(mass2*position2)+

(mass3*position3) / (mass 1+2+3)

now find X using the numbers above ( masses are the 30,50,10) and their respective

positions (.31,1.39,1.65)

after u find X

find X again, this time substitute the positions values with the new set (.2,.57,.78)

after u get these two X values, basically u have found two different center of masses for

the person, so by subtracting these two values u should get his change in position

u should get .59 as ur answer