In which of the following options is the amount of gold identical in the two coins? (Pure gold is 24 carat)
Understanding Gold Purity (Carat)
Pure gold is defined as 24 carat. The carat system indicates the proportion of pure gold in an alloy. A coin or piece of jewelry that is less than 24 carat contains a mixture of gold and other metals.
To find the amount of pure gold in a metal with a given carat, we use the ratio of its carat value to 24. The formula to calculate the amount of pure gold is:
\(\text{Amount of Pure Gold} = \text{Total Weight of Coin} \times \frac{\text{Carat Value}}{24}\)
Using this formula, we can calculate the amount of pure gold present in each coin described in the options.
Calculating Gold in Each Coin
Let's apply the formula to the coins mentioned in each option:
| Option | Coin 1 Details | Coin 1 Gold Amount | Coin 2 Details | Coin 2 Gold Amount | Identical Gold Amount? |
|---|---|---|---|---|---|
| 1 | 24g coin of 22 carat | \(24 \text{ g} \times \frac{22}{24} = 22 \text{ g}\) | 22g coin of 24 carat | \(22 \text{ g} \times \frac{24}{24} = 22 \text{ g}\) | Yes |
| 2 | 22g coin of 22 carat | \(22 \text{ g} \times \frac{22}{24} = 22 \text{ g} \times \frac{11}{12} \approx 20.17 \text{ g}\) | 24g coin of 24 carat | \(24 \text{ g} \times \frac{24}{24} = 24 \text{ g}\) | No |
| 3 | 22g coin of 22 carat | \(22 \text{ g} \times \frac{22}{24} \approx 20.17 \text{ g}\) | 22g coin of 24 carat | \(22 \text{ g} \times \frac{24}{24} = 22 \text{ g}\) | No |
| 4 | 24g coin of 22 carat | \(24 \text{ g} \times \frac{22}{24} = 22 \text{ g}\) | 24g coin of 24 carat | \(24 \text{ g} \times \frac{24}{24} = 24 \text{ g}\) | No |
Comparing the Results
From the calculations shown in the table:
- In Option 1, the 24g coin of 22 carat contains 22g of pure gold, and the 22g coin of 24 carat also contains 22g of pure gold. The amounts are identical.
- In Option 2, the amounts of pure gold are approximately 20.17g and 24g, which are not identical.
- In Option 3, the amounts of pure gold are approximately 20.17g and 22g, which are not identical.
- In Option 4, the amounts of pure gold are 22g and 24g, which are not identical.
Therefore, the amount of gold is identical only in the coins described in Option 1.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
