Question 1 to 8.
1.A man throws a ball vertically upward with an initial speed of 20ms^{-1}. What is the maximum height reached by the ball and how long does it take
to return to the point it was thrown? (a) 20 s (b) 20.4 s (c )0.20~s(d)2.04 s
2. An object sliding freely down an inclined plane has acceleration due to gravity equal to
(a) g sin ) (b) g Cos 8 (c) g tan 0 (d) yisin 0
3. Which of the following is the dimension of an Internal Energy?
(a)ML^{2}T^{3}(b)\overline{L}T^{2}T^{2}(c~ML^{2}T^{3}(d)ML^{2}T^{2}
4. All are types of motion except;
(a) Rectilinear (b) Rotary (c) Circular (d) Centric
5. The acceleration due to gravity depends on the following except...
(a) Latitude (b) Altitude (c) Local effects (d) All of the above
6. Convert 2.5~gmm^{-2}to~kgm^{-2}
(a)250 kgm² 2.500~kgm^{-7} (c) 0.025~kgm^{-2} (d) 2500~kgm^{-2}
7. The period of a simple pendulum 7, depends on the mass of the bob 'm', length of the length of the thread 1, and acceleration due to gravity \prime g^{\prime}. Use method of dimensions to find an expression for the period 7.
(a)T=k(l/g)^{1/2}(b)T=k(l/g)^{-1/2}(c ) T=k(l/g) (d) T=l(k/g)^{12}
8. A river is wide and flowing 3Km/hr. if a man who
can swin at a speed of 5km/hr in the pool has to cross the river, what is direction he must head in order to reach a point directly opposite the standing point.
(a) 5.3 km/hr (b) 15 km/hr (c) 8.0 km/hr (d) 5.84 km/hr
1. The maximum height reached by the ball can be found using the formula for maximum height in vertical projectile motion:
h = (v^2)/(2g)
where v is the initial velocity (20 m/s) and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get:
h = (20^2)/(2*9.8) = 20.41 m
So, the maximum height reached by the ball is 20.41 m.
To find the time taken for the ball to return to the point it was thrown, we can use the formula for time of flight in vertical projectile motion:
t = 2v/g
Plugging in the values, we get:
t = 2*20/9.8 = 4.08 s
So, it takes 4.08 seconds for the ball to return to the point it was thrown.
The correct answer is (b) 20.4 s.
2. The acceleration due to gravity on an inclined plane can be calculated using:
a = g*sin(theta)
where g is the acceleration due to gravity and theta is the angle of the inclined plane.
So, the correct answer is (a) g*sin(theta).
3. The dimension of internal energy can be represented as:
(a) ML^2T^(-2)
So, the correct answer is (a) ML^2T^(-2).
4. The types of motion are:
- Rectilinear: Motion along a straight line
- Rotary: Motion along a circular path
- Circular: Motion in a circle
- Centric: Motion towards or away from a center
So, the correct answer is (d) Centric.
5. The acceleration due to gravity, g, does not depend on latitude, altitude or local effects. It is a constant value on Earth, approximately 9.8 m/s^2.
So, the correct answer is (d) All of the above.
6. To convert 2.5 g/mm^2 to kg/m^2, we need to multiply by a conversion factor of 10^-3 kg in 1 g and 10^6 mm^2 in 1 m^2:
2.5 g/mm^2 * (10^-3 kg/1 g) * (10^6 mm^2/1 m^2) = 2.5 * 10^-3 * 10^6 kg/m^2 = 2500 kg/m^2
So, the correct answer is (d) 2500 kg/m^2.
7. The period of a simple pendulum can be found using the formula:
T = 2π√(l/g)
where T is the period, l is the length of the thread, and g is the acceleration due to gravity.
Using the method of dimensions, we can determine the relationship between T, l, and g:
T = k(l/g)^a
where k is a constant and a is an exponent.
Comparing the dimensions of both sides of the equation, we can determine the values of a and the correct expression for the period:
[T] = [L]^[1/2] [T]^[1]
From this, we can see that a = 1/2.
So, the correct answer is (a) T = k(l/g)^(1/2).
8. In order to cross the river and reach a point directly opposite the standing point, the man must swim at an angle against the direction of the river flow.
By using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity:
v^2 = (3 km/hr)^2 + (5 km/hr)^2 = 34 km/hr
Then, by using the trigonometric relationship between the angle and the components of velocity:
sin(theta) = (5 km/hr)/(34 km/hr)
theta = sin^(-1)((5 km/hr)/(34 km/hr))
theta ≈ 8.66 degrees
So, the correct answer is (c) 8.0 km/hr.