ii/2//5. two bodies of masses $m_1$ and $m_2$ have same momentum the ratio of their kinetic energy isa. $m_2:m_1$ b. $m_1:m_2$ c. $sqrt{\frac{m_2}{m_1}}$ d. $sqrt{\frac{m_1}{m_2}}$6. the bob of a pendulum of length 2m lies at p. when it reaches q, it loses 10% of its total energy due to air resistance. the velocity at q isa. 6 m/s b. 1 m/s c. 2 m/s d. 8 m/s7. a dancer is rotating on smooth horizontal floor with an angular momentum l. the dancer folds her hands so that her moment of inertia decreases by 25%. the new angular momentum isa. 3l/4 b. l/4 c. l/2 d. l8. if radius of earth is r, then the height h at which value of g becomes one-fourth isa. r/4 b. 3r/4 c. r d. r/89. if mass of the earth is doubled and its radius is halved then new acceleration due to gravity isa. 8g b. 4g c. g d. 16g10. an aeroplane gets its upward lift due to a phenomenon described by thea. archimedes principle b. bernoullis principlec. buoyancy principle d. pascal law11. in a simple harmonic oscillator, at the mean positiona. kinetic energy is minimum, potential energy is maximumb. both kinetic and potential energies are maximumc. kinetic energy is maximum, potential energy is minimumd. both kinetic and potential energies are minimum12. the distance between a node and adjoining antinode isa. $lambda/4$ b. $lambda/2$ c. $lambda/3$ d. $3lambda/4$assertion and reason typein the following questions, a statement of assertion (a) is followed by a statement of reason (r). mark the correct choice as :a. both a and r are true and r is the correct explanation of a.b. both a and r are true and r is not the correct explanation of a.c. if a is true but r is false. d. if both a and r are false.13. assertion (a) : on a rainy day, it is difficult to drive a car or bus at high speed.reason (r) : the value of coefficient of friction is lowered due to wetting of the surface.assertion (a) : a planet moves faster, when it is closer to the sun in its orbit and vice-versa.reason (a) : in orbit of planet is constant.

Question

ii/2//5.  two bodies of masses $m_1$ and $m_2$ have same momentum the ratio of their kinetic energy isa.  $m_2:m_1$  b.  $m_1:m_2$  c.  $sqrt{\frac{m_2}{m_1}}$  d.  $sqrt{\frac{m_1}{m_2}}$6.  the bob of a pendulum of length 2m lies at p. when it reaches q, it loses 10% of its total energy due to air resistance. the velocity at q isa.  6 m/s  b.  1 m/s  c.  2 m/s  d.  8 m/s7.  a dancer is rotating on smooth horizontal floor with an angular momentum l. the dancer folds her hands so that her moment of inertia decreases by 25%. the new angular momentum isa.  3l/4  b.  l/4  c.  l/2  d.  l8.  if radius of earth is r, then the height h at which value of g becomes one-fourth isa.  r/4  b.  3r/4  c.  r  d.  r/89.  if mass of the earth is doubled and its radius is halved then new acceleration due to gravity isa.  8g  b.  4g  c.  g  d.  16g10. an aeroplane gets its upward lift due to a phenomenon described by thea.  archimedes principle  b.  bernoullis principlec.  buoyancy principle  d.  pascal law11. in a simple harmonic oscillator, at the mean positiona.  kinetic energy is minimum, potential energy is maximumb.  both kinetic and potential energies are maximumc.  kinetic energy is maximum, potential energy is minimumd.  both kinetic and potential energies are minimum12. the distance between a node and adjoining antinode isa.  $lambda/4$  b.  $lambda/2$  c.  $lambda/3$  d.  $3lambda/4$assertion and reason typein the following questions, a statement of assertion (a) is followed by a statement of reason (r). mark the correct choice as :a.  both a and r are true and r is the correct explanation of a.b.  both a and r are true and r is not the correct explanation of a.c.  if a is true but r is false.  d.  if both a and r are false.13. assertion (a) : on a rainy day, it is difficult to drive a car or bus at high speed.reason (r) : the value of coefficient of friction is lowered due to wetting of the surface.assertion (a) : a planet moves faster, when it is closer to the sun in its orbit and vice-versa.reason (a) : in orbit of planet is constant.

Accepted Answer

### Question 5
# Explanation:
## Step1: Relate momentum and KE
Kinetic energy $KE = \frac{p^2}{2m}$, where $p$ is momentum.
## Step2: Take ratio of KEs
Given $p_1=p_2=p$, so $\frac{KE_1}{KE_2}=\frac{\frac{p^2}{2m_1}}{\frac{p^2}{2m_2}}=\frac{m_2}{m_1}$
# Answer:
a. $m_2:m_1$

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### Question 6
# Explanation:
## Step1: Define initial total energy
At P, total energy $E = mgh$, where $h=2\ 	ext{m}$ (vertical drop from P to Q).
## Step2: Calculate remaining energy at Q
90% of energy remains: $0.9E = \frac{1}{2}mv^2$
## Step3: Substitute E and solve for v
$0.9 	imes mg 	imes 2 = \frac{1}{2}mv^2$
Cancel $m$, $g=10\ 	ext{m/s}^2$:
$0.9 	imes 10 	imes 2 = \frac{1}{2}v^2$
$18 = \frac{v^2}{2} \implies v^2=36 \implies v=6\ 	ext{m/s}$
# Answer:
a. $6\ 	ext{m/s}$

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### Question 7
# Explanation:
## Step1: Recall angular momentum law
In absence of external torque, angular momentum $L$ is conserved.
# Answer:
d. $L$

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### Question 8
# Explanation:
## Step1: Gravitational acceleration formula
$g = \frac{GM}{R^2}$, new $g' = \frac{GM}{(R+h)^2}$
## Step2: Set $g' = \frac{g}{4}$ and solve
$\frac{GM}{(R+h)^2} = \frac{1}{4} 	imes \frac{GM}{R^2}$
Cancel $GM$, take square roots:
$\frac{1}{R+h} = \frac{1}{2R} \implies R+h=2R \implies h=R$
# Answer:
c. $R$

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### Question 9
# Explanation:
## Step1: Gravitational acceleration formula
$g = \frac{GM}{R^2}$
## Step2: Substitute new mass and radius
New $M'=2M$, $R'=\frac{R}{2}$:
$g' = \frac{G(2M)}{(\frac{R}{2})^2} = \frac{2GM}{\frac{R^2}{4}} = 8 	imes \frac{GM}{R^2} = 8g$
# Answer:
a. $8g$

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### Question 10
# Answer:
b. Bernoulli's principle
# Brief Explanations:
Air moves faster over the curved upper wing surface, creating lower pressure than the slower-moving air under the wing. This pressure difference generates upward lift, described by Bernoulli's principle.

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### Question 11
# Answer:
c. Kinetic energy is maximum, potential energy is minimum
# Brief Explanations:
In simple harmonic motion, the mean position has the highest velocity (max kinetic energy) and zero displacement from equilibrium (min potential energy, defined relative to equilibrium).

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### Question 12
# Answer:
a. $\lambda/4$
# Brief Explanations:
In standing waves, the distance between a node (zero displacement) and the nearest antinode (maximum displacement) is one-fourth of the wavelength ($\lambda$).

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### Question 13
# Answer:
a. Both A and R are true and R is the correct explanation of A
# Brief Explanations:
Wetting of road surfaces on rainy days reduces the coefficient of friction between tires and the road, making it harder to maintain traction and control, so both the assertion and reason are true, and the reason explains the assertion.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 5

Step1: Relate momentum and KE

Step2: Take ratio of KEs

Step1: Define initial total energy

Step2: Calculate remaining energy at Q

Step3: Substitute E and solve for v

Step1: Recall angular momentum law

Answer:

Question 6