To tackle this problem, we need to analyze the situation step by step. We have a string that is initially 1 meter hanging and 3 meters lying flat on the table. The burning starts from both ends, with the burning rate at point A being five times that at point B. Given that the burning rate at B is 20 cm/sec, we can derive the burning rate at A and then determine when slipping occurs.

Understanding the Burning Rates

First, let's establish the burning rates:

• The burning rate at B is given as 20 cm/sec.
• Since the burning rate at A is five times that of B, we can calculate it as follows:

Burning rate at A = 5 × 20 cm/sec = 100 cm/sec.

Calculating the Lengths of the String

Next, we need to consider how the lengths of the string change over time as it burns. Initially, we have:

• Length of string hanging (L_h) = 1 m = 100 cm
• Length of string on the table (L_t) = 3 m = 300 cm

The total length of the string is:

Total Length = L_h + L_t = 100 cm + 300 cm = 400 cm.

Time Calculation for Burning

Now, let’s calculate the time it takes for the string to burn completely from both ends. The string will slip when the entire length of the hanging part has burned away. We need to find out how long it takes for the hanging part to burn completely.

Burning the Hanging Part

The hanging part of the string is 100 cm long, and it burns at a rate of 100 cm/sec. Therefore, the time taken to burn the hanging part is:

Time to burn hanging part = Length of hanging part / Burning rate at A = 100 cm / 100 cm/sec = 1 sec.

Burning the Table Part

Simultaneously, the part of the string on the table is also burning. The burning rate at B is 20 cm/sec, and the length of the table part is 300 cm. The time taken to burn the table part is:

Time to burn table part = Length of table part / Burning rate at B = 300 cm / 20 cm/sec = 15 sec.

Determining When Slipping Occurs

Slipping occurs when the entire hanging part has burned away. Since we calculated that the hanging part burns completely in 1 second, we can conclude that slipping will occur at:

Time of slipping = 1 second.

Final Answer

Based on the options provided, the correct answer is:

• 1) 0001

Thus, the time when slipping occurs is 1 second. This means that after 1 second, the entire hanging part of the string will have burned away, leading to slipping.