Physics Quiz 0

A body of mass 20 kg moving with a speed of 10 m/s on a horizontal smooth surface collides with a massless spring of spring constant 5 N/m. If the mass stops after collision, distance of compression of the spring will be :

• 10m

• 50m

• 5m

• 20m

Answer explanation

0.5kx²=0.5mv²

The length of a body is measured as 3.51 m. If the accuracy is 0.01 m, then the percentage error in the measurement is :

• 0.035%

• 351%

• 1%

• 0.28%

The dimensional formula for Moment of Inertia :

• ML^-1T^-1

• ML²T^-2

• ML²

• M²L

Answer explanation

Which one of the following is a scalar quantity ?

• Speed

• Velocity

• Displacement

• Linear momentum

When a car takes a sudden left turn on a curved road, passengers are pushed towards the right due to :

• absence of inertia

• inertia of direction

• inertia of motion

• inertia of rest

A spring of force constant k is cut into two pieces such that the length of one piece is double the length of the other. Then the longer piece will have a force constant of :

• 6k

• 2.5k

• 0.5k

• 1.5k

Answer explanation

1. 
   Step 1: Define the lengths of the pieces
   Let the total length of the original spring be L. When the spring is cut into two pieces such that one piece is double the length of the other, we can denote the lengths of the two pieces as follows:
   - Let the length of the shorter piece be x.
   - Therefore, the length of the longer piece will be 2x.

2. Step 2: Relate the lengths to the total length
   Since the total length of the spring is L, we can write the equation:
   x+2x=L
   This simplifies to:
   3x=L
   From this, we can find x:
   x=L/3
   Thus, the lengths of the two pieces are:
   - Shorter piece: x=L/3
   - Longer piece: 2x=2L/3

3. Step 3: Understand the relationship between force constant and length
   The force constant k of a spring is inversely proportional to its length. The relationship can be expressed as:
   k′=k/length of the spring
   where k′ is the new force constant after cutting the spring.

4. Step 4: Calculate the new force constant for the longer piece
   For the longer piece, which has a length of 2L/3, we can find its new force constant klong:
   klong=k/(2L/3)=3k/2L

5. Step 5: Relate the original force constant to the new one
   Since the original spring had a force constant k when it had a length L, we can express the original force constant as:
   k=k'/L

   
   

Moment of inertia of a solid cylinder of Mass M, length l and radius r about its own axis is:

• (1/2) Mr^2

• (1/4) Mr^2

• Mr^2

• (1/3) Mr^2

If the length of the simple pendulum is increased by 44% from its original length,

calculate the percentage increase in time period of the pendulum.

Answer explanation

Given- length of Simple pendulum increased by 44%

we know T=2π⋅√lg

Since there is a change of 4% in the length Then we will use normal analysis.

Let when length increased by 44%⇒ length ℓ′=1.44ℓ and Time period be T′

T′=2π√(1.44l/g)

=2π√l/g×(1.2)

T′=T×(1.2)=1.2T

% change =T′−TT×100=0.2TT×100=20%

An object is thrown with initial speed 5 m/s with an angle of projection 30°. Calculate

the maximum height reached ( take g= 9.8 ms^-2 ) (round up your answer to 3 significant figure with unit)

An object is thrown with initial speed 5 m/s with an angle of projection 30°. Calculate

the maximum horizontal range. ( take g= 9.8 ms^-2 ) (round up your answer to 3 significant figure with unit)

Answer explanation