Question

can anybody solve this​

Answer 1

1. The dimensions of Universal gravitational constant is(G) are ?

Solution:-  According to Newton's law of gravitation,

$F=G\frac{m_1m_2}{r^2}\\\;\\G=F\frac{r^2}{m_1m_1}$

Dimension of Force(F) = MLT⁻²

Dimension of Distance(r) = L

Dimension of Mass(m₁, and m₂) = M

$G=\frac{[MLT^{-2}][L^2]}{[M][M]}\\\;\\G=[M^{-1}L^3T^{-2}]$

Hence Option ii) is correct

2.  The angle between two vectors -2i+3j+k  and i+2j-4k is ?

Solution:- Applying the formula for angle between two vectors,

$\cos\theta=\frac{l_1l_2+m_1m_2+n_1n_2}{(\sqrt{{l_1}^2+{m_1}+{n_1}^2}).(\sqrt{{l_2}^2+{m_2}+{n_2}^2})}\\\;\\\cos\theta=\frac{-2+6-4}{(\sqrt{{l_1}^2+{m_1}+{n_1}^2}).(\sqrt{{l_2}^2+{m_2}+{n_2}^2})}\\\;\\\cos\theta=0\\\;\\\theta=90^{\circ}$

Hence option ii) is correct

3.) An athlete completes one round of a circular track of radius R in 40 sec. What is the displacement at the end of 2 min 20 seconds ?

Solution:- Time = 2 min 20 seconds = 140 seconds

Number of Round in 140 seconds = 140/40

                                                        = 3.5

Thus athlete completes 3 and half rounds in 2 min 20 seconds. Thus his starting point and ending point  will be on opposite side on diameter line, which will be equal of diameter of the circle. Hence there will be 2r displacement.

Thus option ii) is correct.

4.) A stone is thrown vertically upwards with an initial velocity of 30m/s. The time taken for the stone to rise to its maximum height is,

Solution:- Using newton's third equation of motion,

v = u - gt

0 = u - gt

t = u/g

t = 30/9.8

t = 3.061 s

Hence option iv)  is correct

5.) If a constant force is applied on a mass, it moves with uniform ?

Solution:-  Consider the Equation

F = ma

Here m = mass is constant and applied force is also constant as given in question. Thus it will result as Uniform a = acceleration.

Hence option ii) is correct

6.) A light and a heavy body have equal momentum. Which one has greater kinetic energy(K.E.) ?

Solution:- Consider the relation between momentum and Kinetic energy

K = p²/2m

It suggest that K is inversely proportional to mass(m). Thus lighter the body, greater the kinetic energy(K.E.)

Hence option i) is correct.

7.) The kinetic energy of a given body is doubled, its momentum will ?

Solution:- Consider the relation between momentum and Kinetic energy

K = p²/2m

Considering for two situations(K₂ = 2K₁)

p₁²/p₂² = K₁/K₂

p₁²/p₂²  = K₁/2K₁

p₂ = √2p₁

Thus momentum will be √2 times of the previous momentum

Hence option iv) is correct

8.) A ball is thrown up at an angle 30° with the horizontal. If R and H represent its horizontal range and  maximum height reached, then

Solution:-

Angle of projectile = 30°

Horizontal Range = R

Maximum Height = H

We know that,

$R=\frac{u^2\sin2\theta}{g}$

$H=\frac{u^2\sin^2\theta}{2g}$

Now,

$\frac{R}{H}=\frac{\sin2\theta}{\frac{\sin^2\theta}{2}}\\\;\\\frac{R}{H}=\frac{2\sin2\theta}{\sin^2\theta}\\\;\\\frac{R}{H}=\frac{2.2\sin\theta\cos\theta}{\sin\theta}\\\;\\\frac{R}{H}=4\tan\theta\\\;\\\frac{R}{H}=4\times\frac{1}{\sqrt{3}}\\\;\\R=\frac{4}{\sqrt{3}}H$

Hence option iv) is correct.

9.) Energy stored per unit volume in a stretched wire is ?

Solution:-

Formula for energy Density is,

U = 1/2 × Stress × Strain

Hence option iv) is correct.

10.) A cyclist bends while taking turn to ?

Solution:-A cyclist bends while taking turn to generate the required centripetal force  to counter act the effect of outward torque which leads to skid off or topple.. This force is directed towards center of the curved radius.

Here option ii) is correct.

11.) The angular velocity of the seconds hand of a clock is:

Solution:- Since seconds hand completes its round of 2π radian in 60 seconds,

Angular Velocity = 2π/60

                            = π/30 rad/s

Hence option iii) is correct.

12.) a person standing on a rotating stool spreading his arms. He suddenly contracts his arms. His:

Solution:- While spreading his hands, mass of the system  is distributed more about the axis so moment of inertia will be high. But as soon as he contracts his arms, the mass distribution about the axis will have less radius with respect to center of mass. Thus moment of inertia will decrease.

Thus option iii) is correct

13.) The moon's radius is 1/4 times that of the earth and its mass 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is :

Solution:-

Acceleration due to gravity on earth,

$g=G\frac{M_e}{R_e^2}\\\;$

Acceleration due to gravity on moon,

$g_m=G\frac{M_m}{{R^2_m}}$

Now,

$\frac{g}{g_m}=\frac{M_e}{M_m}\times(\frac{R_m}{R_e})^2\\\;\\\text{Putting}\;\;M_m=\frac{M_e}{80}\;\;\text{and}\;\;R_m=\frac{R_e}{4}\\\;\\\implies\;\frac{g}{g_m}=80\times\frac{1}{4^2}\\\;\\\implies\;\frac{g}{g_m}=5\\\;\\\implies\;g_m=\frac{g}{5}$

Hence option ii) is correct.

14.) The displacement of an oscillator is given by x = 5sin(10πt+π). The phase of the particle at t = 1 ?

Solution:-

Phase of the particle,

Ф = 10πt+π

Putting t = 1,

Ф = 10π+π

Ф = 11π

Hence option iv) is correct