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Contributing to mining algorithms using low-powered devices is one of the principal concerns in the growth of the Internet of Things (IoT) paradigm. To address this limitation, we introduce a new concept of allocating mining devices based on their computation power in sharding-based blockchain systems for the IoT. This study proposes two scenarios based on different ways of partitioning the transactions into the disjoint shards: Scenario 1 (Number of processors are equally distributed among shards); Scenario 2 (Number of processors are distributed among shards using computation power-based criterion). We also adopt an adversary model to obtain the fraction of participating processors that must be compromised by the adversaries to compromise our proposed method of sharding based blockchain networks. Our results demonstrate that the total computation cost of the entire system increases when the computing cost for verifying signatures and the number of shards increases. We observe that the total reward of each processor increases when the number of less powerful processors increases. The total number of mined processors of each shard decreases with a high number of less powerful processors. Thus, the total reward of the entire network is distributed among a few processors. We demonstrate that our new method of allocating mining devices based on their computation power (Scenario 2) provides fair reward distribution. Additionally, when the total number of processors in a network is higher than 500, each processor's total reward increment shows an insignificant change. However, when the total number of processors is lower than 500, each processor's total reward shows an upward linear trend and contradicts the assumption of Scenario 1. Thus, our results show that the proposed model (Scenario 2) is more suitable for allocating mining devices based on their computation power in sharding-based blockchain systems for IoT, especially devices with different computational capabilities or processors with selfish behavior. This concept motivates powerful processors to verify and validate new transactions to be added to the blockchain.